Koblitz, Neal 1948
Overview
Works:  47 works in 360 publications in 5 languages and 8,864 library holdings 

Genres:  Conference papers and proceedings Biography History Textbooks Filmed lectures Nonfiction films 
Roles:  Author, Translator, Editor, Thesis advisor, Creator 
Classifications:  QA241, 512.74 
Publication Timeline
.
Most widely held works about
Neal Koblitz
 Random curves : journeys of a mathematician by Neal Koblitz( Book )
Most widely held works by
Neal Koblitz
A course in number theory and cryptography by
Neal Koblitz(
Book
)
57 editions published between 1987 and 2013 in 3 languages and held by 1,440 WorldCat member libraries worldwide
The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasizing estimates of the efficiency of the techniques that arise from the theory. A special feature is the inclusion of recent application of the theory of elliptic curves. Extensive exercises and careful answers have been included in all of the chapters. Because number theory and cryptography are fastmoving fields, this new edition contains substantial revisions and updated references
57 editions published between 1987 and 2013 in 3 languages and held by 1,440 WorldCat member libraries worldwide
The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, that have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasizing estimates of the efficiency of the techniques that arise from the theory. A special feature is the inclusion of recent application of the theory of elliptic curves. Extensive exercises and careful answers have been included in all of the chapters. Because number theory and cryptography are fastmoving fields, this new edition contains substantial revisions and updated references
Introduction to elliptic curves and modular forms by
Neal Koblitz(
Book
)
42 editions published between 1984 and 2012 in 4 languages and held by 1,052 WorldCat member libraries worldwide
"The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the HasseWeil Lfunction and the conjecture of Birch and SwinnertonDyer. The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves."Page 4 de la couverture
42 editions published between 1984 and 2012 in 4 languages and held by 1,052 WorldCat member libraries worldwide
"The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the HasseWeil Lfunction and the conjecture of Birch and SwinnertonDyer. The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves."Page 4 de la couverture
Padic numbers, padic analysis, and zetafunctions by
Neal Koblitz(
Book
)
47 editions published between 1977 and 2014 in 4 languages and held by 939 WorldCat member libraries worldwide
These lecture notes are intended as an introduction to padic analysis on the elementary level. For this reason they presuppose as little background as possi ble. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topolog ical spaces. The purpose of this book is twofold: to develop some basic ideas of padic analysis, and to present two striking applications which, it is hoped, can be as effective pedagogically as they were historically in stimulating interest in the field. The first of these applications is presented in Chapter II, since it only requires the most elementary properties of Q ; this is Mazur's construction by p means of padic integration of the KubotaLeopoldtpadic zetafunction, which "padically interpolates" the values of the Riemann zetafunction at the negative odd integers. My treatment is based on Mazur's Bourbaki notes (unpublished)
47 editions published between 1977 and 2014 in 4 languages and held by 939 WorldCat member libraries worldwide
These lecture notes are intended as an introduction to padic analysis on the elementary level. For this reason they presuppose as little background as possi ble. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topolog ical spaces. The purpose of this book is twofold: to develop some basic ideas of padic analysis, and to present two striking applications which, it is hoped, can be as effective pedagogically as they were historically in stimulating interest in the field. The first of these applications is presented in Chapter II, since it only requires the most elementary properties of Q ; this is Mazur's construction by p means of padic integration of the KubotaLeopoldtpadic zetafunction, which "padically interpolates" the values of the Riemann zetafunction at the negative odd integers. My treatment is based on Mazur's Bourbaki notes (unpublished)
Algebraic aspects of cryptography by
Neal Koblitz(
Book
)
29 editions published between 1997 and 2004 in English and held by 742 WorldCat member libraries worldwide
This is a textbook for a course (or selfinstruction) in cryptography with emphasis on algebraic methods. The first half of the book is a selfcontained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half  "hidden monomial" systems, combinatorialalgebraic systems, and hyperelliptic systems  has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security. From the reviews: " ... This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. ... Overall, this is an excellent expository text, and will be very useful to both the student and researcher." M.V.D. Burmester, Mathematical Reviews 2002 " ... I think this book is a very inspiring book on cryptography. It goes beyond the traditional topics (most of the cryptosystems presented here are first time in a textbook, some of Patarin's work is not published yet). This way the reader has the feeling how easy to suggest a cryptosystem, how easy to break a safe looking system and hence how hard to trust one. The interested readers are forced to think together with their researchers and feel the joy of discovering new ideas. At the same time the importance of "hardcore" mathematics is emphasized and hopefully some application driven students will be motivated to study theory." P. Hajnal, Acta Scientiarum Mathematicarum 64.1998 " ... Overall, the book is highly recommended to everyone who has the requisite mathematical sophistication." E. Leiss, Computing Reviews 1998
29 editions published between 1997 and 2004 in English and held by 742 WorldCat member libraries worldwide
This is a textbook for a course (or selfinstruction) in cryptography with emphasis on algebraic methods. The first half of the book is a selfcontained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half  "hidden monomial" systems, combinatorialalgebraic systems, and hyperelliptic systems  has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security. From the reviews: " ... This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. ... Overall, this is an excellent expository text, and will be very useful to both the student and researcher." M.V.D. Burmester, Mathematical Reviews 2002 " ... I think this book is a very inspiring book on cryptography. It goes beyond the traditional topics (most of the cryptosystems presented here are first time in a textbook, some of Patarin's work is not published yet). This way the reader has the feeling how easy to suggest a cryptosystem, how easy to break a safe looking system and hence how hard to trust one. The interested readers are forced to think together with their researchers and feel the joy of discovering new ideas. At the same time the importance of "hardcore" mathematics is emphasized and hopefully some application driven students will be motivated to study theory." P. Hajnal, Acta Scientiarum Mathematicarum 64.1998 " ... Overall, the book is highly recommended to everyone who has the requisite mathematical sophistication." E. Leiss, Computing Reviews 1998
Number theory related to Fermat's last theorem : proceedings of the conference sponsored by the Vaughn Foundation by Conference on Number Theory Related to Fermat's Last Theorem(
Book
)
19 editions published in 1982 in English and Undetermined and held by 399 WorldCat member libraries worldwide
19 editions published in 1982 in English and Undetermined and held by 399 WorldCat member libraries worldwide
Padic analysis : a short course on recent work by
Neal Koblitz(
Book
)
20 editions published in 1980 in English and Undetermined and held by 392 WorldCat member libraries worldwide
This introduction to recent work in padic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of padic numbers and the padic analog of the complex number field, power series and Newton polygons), the author develops the properties of padic Dirichlet Lseries using padic measures and integration. padic gamma functions are introduced, and their relationship to Lseries is explored. Analogies with the corresponding complex analytic case are stressed
20 editions published in 1980 in English and Undetermined and held by 392 WorldCat member libraries worldwide
This introduction to recent work in padic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of padic numbers and the padic analog of the complex number field, power series and Newton polygons), the author develops the properties of padic Dirichlet Lseries using padic measures and integration. padic gamma functions are introduced, and their relationship to Lseries is explored. Analogies with the corresponding complex analytic case are stressed
Advances in cryptology, CRYPTO '96 : 16th annual international cryptology conference, Santa Barbara, California, USA, August
1822, 1996 : proceedings by
Neal Koblitz(
Book
)
33 editions published between 1996 and 2001 in English and held by 338 WorldCat member libraries worldwide
"This book constitutes the refereed proceedings of the 16th Annual International Cryptology Conference, CRYPTO '96, held in Santa Barbara, California, USA, in August 1996 under the sponsorship of the International Association for Cryptologic Research (IACR). The 30 revised full papers presented in the volume were selected from a total of 130 submissions; they are organized in topical sections on hashing and authentication, new systems, cryptoanalysis, hard bits, signatures, zero knowledge, symmetric systems, DiffieHellman oracle, quantum cryptography, stream ciphers, and secret sharing. All in all, this book is a current report on the stateoftheart in the field."PUBLISHER'S WEBSITE
33 editions published between 1996 and 2001 in English and held by 338 WorldCat member libraries worldwide
"This book constitutes the refereed proceedings of the 16th Annual International Cryptology Conference, CRYPTO '96, held in Santa Barbara, California, USA, in August 1996 under the sponsorship of the International Association for Cryptologic Research (IACR). The 30 revised full papers presented in the volume were selected from a total of 130 submissions; they are organized in topical sections on hashing and authentication, new systems, cryptoanalysis, hard bits, signatures, zero knowledge, symmetric systems, DiffieHellman oracle, quantum cryptography, stream ciphers, and secret sharing. All in all, this book is a current report on the stateoftheart in the field."PUBLISHER'S WEBSITE
A course in mathematical logic for mathematicians by
I︠U︡. I Manin(
Book
)
11 editions published between 2009 and 2010 in English and held by 183 WorldCat member libraries worldwide
"A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal languages and proceeds to a discussion of proof theory. It then presents several highlights of 20th century mathematical logic, including theorems of Godel and Tarski, and Cohen's theorem on the independence of the continuum hypothesis. A unique feature of the text is a discussion of quantum logic." "The exposition then moves to a discussion of computability theory that is based on the notion of recursive functions and stresses numbertheoretic connections. The text presents a complete proof of the theorem of DavisPutnamRobinsonMatiyasevich as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is also treated"Jacket
11 editions published between 2009 and 2010 in English and held by 183 WorldCat member libraries worldwide
"A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal languages and proceeds to a discussion of proof theory. It then presents several highlights of 20th century mathematical logic, including theorems of Godel and Tarski, and Cohen's theorem on the independence of the continuum hypothesis. A unique feature of the text is a discussion of quantum logic." "The exposition then moves to a discussion of computability theory that is based on the notion of recursive functions and stresses numbertheoretic connections. The text presents a complete proof of the theorem of DavisPutnamRobinsonMatiyasevich as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is also treated"Jacket
Towards a quartercentury of public key cryptography by
Neal Koblitz(
Book
)
7 editions published between 2000 and 2011 in English and held by 63 WorldCat member libraries worldwide
Towards a QuarterCentury of Public Key Cryptography brings together in one place important contributions and uptodate research results in this fast moving area. Towards a QuarterCentury of Public Key Cryptography serves as an excellent reference, providing insight into some of the most challenging research issues in the field
7 editions published between 2000 and 2011 in English and held by 63 WorldCat member libraries worldwide
Towards a QuarterCentury of Public Key Cryptography brings together in one place important contributions and uptodate research results in this fast moving area. Towards a QuarterCentury of Public Key Cryptography serves as an excellent reference, providing insight into some of the most challenging research issues in the field
Single variable calculus : early transcendentals by
David Guichard(
)
in English and held by 49 WorldCat member libraries worldwide
"An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available."Open Textbook Library
in English and held by 49 WorldCat member libraries worldwide
"An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available."Open Textbook Library
Gauge field theory and complex geometry by
I︠U︡. I Manin(
Book
)
6 editions published between 1997 and 2010 in English and held by 37 WorldCat member libraries worldwide
From the reviews: " ... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics)"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov
6 editions published between 1997 and 2010 in English and held by 37 WorldCat member libraries worldwide
From the reviews: " ... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics)"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov
A course in mathematical logic by
I︠U︡. I Manin(
Book
)
4 editions published in 1977 in English and Undetermined and held by 32 WorldCat member libraries worldwide
This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a subclass of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities
4 editions published in 1977 in English and Undetermined and held by 32 WorldCat member libraries worldwide
This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a subclass of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities
Mathematics and physics by
I︠U︡. I Manin(
Book
)
5 editions published between 1981 and 1983 in English and held by 29 WorldCat member libraries worldwide
5 editions published between 1981 and 1983 in English and held by 29 WorldCat member libraries worldwide
Random curves : journeys of a mathematician by
Neal Koblitz(
Book
)
16 editions published between 2008 and 2014 in English and held by 27 WorldCat member libraries worldwide
These autobiographical memoirs of Neal Koblitz, coinventor of one of the two most popular forms of encryption and digital signature, cover many topics besides his own personal career in mathematics and cryptography  travels to the Soviet Union, Latin America, Vietnam and elsewhere, political activism, and academic controversies relating to math education, the C.P. Snow twoculture problem, and mistreatment of women in academia. The stories speak for themselves and reflect the experiences of a student and later a scientist caught up in the tumultuous events of his generation
16 editions published between 2008 and 2014 in English and held by 27 WorldCat member libraries worldwide
These autobiographical memoirs of Neal Koblitz, coinventor of one of the two most popular forms of encryption and digital signature, cover many topics besides his own personal career in mathematics and cryptography  travels to the Soviet Union, Latin America, Vietnam and elsewhere, political activism, and academic controversies relating to math education, the C.P. Snow twoculture problem, and mistreatment of women in academia. The stories speak for themselves and reflect the experiences of a student and later a scientist caught up in the tumultuous events of his generation
Spectral theory and analytic geometry over nonArchimedean fields by
Vladimir G Berkovich(
Book
)
3 editions published in 1990 in English and held by 24 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 24 WorldCat member libraries worldwide
Mathematics under hardship conditions in the Third World by
Neal Koblitz(
Visual
)
2 editions published between 1991 and 1992 in English and held by 16 WorldCat member libraries worldwide
Koblitz examines such questions as why mathematics research flourishes in Vietnam, while other countries contend with "brain drain" to the U.S. and Europe. He relates stories of problems that are faced and people that are resourceful. He suggests specific actions that can be taken to help keep mathematics alive and growing the the Third World
2 editions published between 1991 and 1992 in English and held by 16 WorldCat member libraries worldwide
Koblitz examines such questions as why mathematics research flourishes in Vietnam, while other countries contend with "brain drain" to the U.S. and Europe. He relates stories of problems that are faced and people that are resourceful. He suggests specific actions that can be taken to help keep mathematics alive and growing the the Third World
Elliptic curve public key cryptosystems by
A. J Menezes(
Book
)
6 editions published between 1993 and 2002 in English and Undetermined and held by 15 WorldCat member libraries worldwide
Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an uptodate and selfcontained treatment of elliptic curvebased public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems. Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject
6 editions published between 1993 and 2002 in English and Undetermined and held by 15 WorldCat member libraries worldwide
Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an uptodate and selfcontained treatment of elliptic curvebased public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems. Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject
Transcendental numbers by
A. B Shidlovskiĭ(
Book
)
8 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
8 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
The Riemann zetafunction by
A. A Karatsuba(
Book
)
4 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
The Riemann ZetaFunction (De Gruyter Expositions in Mathematics)
4 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
The Riemann ZetaFunction (De Gruyter Expositions in Mathematics)
Calculus : early transcendentals by
David Guichard(
Book
)
3 editions published in 2013 in English and held by 1 WorldCat member library worldwide
"The book covers the standard material in a one variable calculus course for science and engineering."BC Campus website
3 editions published in 2013 in English and held by 1 WorldCat member library worldwide
"The book covers the standard material in a one variable calculus course for science and engineering."BC Campus website
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Related Identities
 Manin, I︠U︡. I. Author
 Zilber, Boris
 Vaughn Foundation Other
 Shidlovskiĭ, A. B. Author
 International Association for Cryptologic Research
 University of California, Santa Barbara Computer Science Department
 IEEE Computer Society Technical Committee on Security and Privacy
 Menezes, Alfred J. Author
 Berkovich, Vladimir G. Author
 CRYPTO 1996 Santa Barbara, Calif
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Associated Subjects
Algebraic number theory Calculus CalculusStudy and teaching Coding theory Combinatorial analysis Computational complexity Computer engineering ComputersAccess control Computer science Computer security Computer software Cryptographers Cryptography Curves, Elliptic Data encryption (Computer science) Data structures (Computer science) Developing countries Engineering Fermat's last theorem Forms, Modular Functional analysis Functions, Zeta Gauge fields (Physics) Geometric quantization Geometry, Algebraic Geometry, Analytic Geometry, Differential Global analysis (Mathematics) Global differential geometry Information theory Logic Logic, Symbolic and mathematical Mathematicians Mathematics MathematicsResearch MathematicsStudy and teaching Number theory Operating systems (Computers) padic analysis padic numbers Physics Public key cryptography Quantum field theory Selberg trace formula Spectral theory (Mathematics) Transcendental numbers Travel United States World politics
Alternative Names
Koblic, N.
Koblic, N. 1948
Koblic, Nil 1948
Koblit︠s︡, N. 1948
Koblits, Neal.
Koblits Neal 1948....
Koblitz, N.
Koblitz, N. 1948
Koblitz, Neal
Koblitz, Neal I.
Koblitz, Neil 1948
Neal Koblitz Amerikaans wiskundige
Neal Koblitz Mathematician, cryptographer
Neal Koblitz mathématicien américain
Neal Koblitz USamerikanischer Mathematiker
Коблиц, Нил.
Нил Коблиц
コブリッツ, N.
コブリッツ, ニール
ニール・コブリッツ
尼爾·科布利茨
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