Kra, Irwin
Overview
Works:  31 works in 232 publications in 2 languages and 5,179 library holdings 

Genres:  Conference papers and proceedings Biography 
Roles:  Editor, Author, Contributor, Other 
Classifications:  QA333, 515.223 
Publication Timeline
.
Most widely held works by
Irwin Kra
Riemann surfaces by
Hershel M Farkas(
Book
)
37 editions published between 1979 and 2003 in English and Undetermined and held by 899 WorldCat member libraries worldwide
The present volume is the culmination often years' work separately and joint ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 19701971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of presentday research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians
37 editions published between 1979 and 2003 in English and Undetermined and held by 899 WorldCat member libraries worldwide
The present volume is the culmination often years' work separately and joint ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 19701971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of presentday research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians
A crash course on Kleinian groups; lectures given at a special session at the January 1974 meeting of the American Mathematical
Society at San Francisco by
American Mathematical Society(
Book
)
30 editions published between 1974 and 2008 in English and held by 469 WorldCat member libraries worldwide
30 editions published between 1974 and 2008 in English and held by 469 WorldCat member libraries worldwide
Complex analysis : in the spirit of Lipman Bers by
Jane Gilman(
Book
)
34 editions published between 2007 and 2013 in English and held by 426 WorldCat member libraries worldwide
"This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complexvalued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and threemanifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers." "The book covers most, if not all, of the material contained in Bers's courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored."Jacket
34 editions published between 2007 and 2013 in English and held by 426 WorldCat member libraries worldwide
"This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complexvalued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and threemanifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers." "The book covers most, if not all, of the material contained in Bers's courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored."Jacket
Riemann surfaces and related topics : proceedings of the 1978 Stony Brook conference by Conference on Riemann Surfaces and Related Topics(
Book
)
18 editions published between 1980 and 1981 in English and Undetermined and held by 421 WorldCat member libraries worldwide
18 editions published between 1980 and 1981 in English and Undetermined and held by 421 WorldCat member libraries worldwide
Automorphic forms and Kleinian groups by
Irwin Kra(
Book
)
19 editions published between 1972 and 1975 in 3 languages and held by 397 WorldCat member libraries worldwide
19 editions published between 1972 and 1975 in 3 languages and held by 397 WorldCat member libraries worldwide
Hilbert's fourth problem by
A. V Pogorelov(
Book
)
5 editions published in 1979 in English and held by 371 WorldCat member libraries worldwide
5 editions published in 1979 in English and held by 371 WorldCat member libraries worldwide
Quasiconformal mappings and Riemann surfaces by
S. L Krushkalʹ(
Book
)
10 editions published in 1979 in English and held by 271 WorldCat member libraries worldwide
10 editions published in 1979 in English and held by 271 WorldCat member libraries worldwide
Theta constants, Riemann surfaces, and the modular group : an introduction with applications to uniformization theorems, partition
identities, and combinatorial number theory by
Hershel M Farkas(
Book
)
14 editions published in 2001 in English and held by 269 WorldCat member libraries worldwide
There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for numbertheoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL}(2,\mathbb{Z})$, which provide another path for insights into number theory. Farkas and Kra, wellknown masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for researchlevel problems. The text is suitable for a graduate course or for independent reading
14 editions published in 2001 in English and held by 269 WorldCat member libraries worldwide
There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for numbertheoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL}(2,\mathbb{Z})$, which provide another path for insights into number theory. Farkas and Kra, wellknown masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for researchlevel problems. The text is suitable for a graduate course or for independent reading
In the tradition of Ahlfors and Bers : proceedings of the First AhlforsBers Colloquium, AhlforsBers Colloquium, November
68, 1998, State University of New York at Stony Brook by AhlforsBers Colloquium(
Book
)
14 editions published in 2000 in English and held by 212 WorldCat member libraries worldwide
14 editions published in 2000 in English and held by 212 WorldCat member libraries worldwide
Selected works of Lipman Bers : papers on complex analysis by
Lipman Bers(
Book
)
13 editions published in 1998 in English and held by 135 WorldCat member libraries worldwide
13 editions published in 1998 in English and held by 135 WorldCat member libraries worldwide
Lipman Bers, a life in mathematics(
Book
)
6 editions published in 2015 in English and held by 73 WorldCat member libraries worldwide
6 editions published in 2015 in English and held by 73 WorldCat member libraries worldwide
On the ring of holomorphic functions on an open Riemann surface by
Irwin Kra(
Book
)
4 editions published between 1966 and 1967 in English and held by 12 WorldCat member libraries worldwide
4 editions published between 1966 and 1967 in English and held by 12 WorldCat member libraries worldwide
Banach algebras of analytic functions on Riemann surfaces by
Irwin Kra(
Book
)
in English and held by 10 WorldCat member libraries worldwide
in English and held by 10 WorldCat member libraries worldwide
Contributions to analysis: a collection of papers dedicated to Lipman Bers by
Lipman Bers(
Book
)
3 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
Lipman Bers : May 22, 1914October 29, 1993(
Book
)
2 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 4 WorldCat member libraries worldwide
Holomorphic functions and moduli : proceedings of a workshop held March 1319, 1986 by
D Drasin(
Book
)
3 editions published in 1988 in English and held by 2 WorldCat member libraries worldwide
The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a miniconference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program
3 editions published in 1988 in English and held by 2 WorldCat member libraries worldwide
The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a miniconference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program
Lectures on quasiconformal mappings by
Lars V Ahlfors(
Book
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a selfcontained treatment of the Beltrami equation, and cover the basic properties of Teichmüller spaces, including the Bers embedding and the Teichmüller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmüller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmüller spaces and provides many references to the vast literature on Teichmüller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a selfcontained treatment of the Beltrami equation, and cover the basic properties of Teichmüller spaces, including the Bers embedding and the Teichmüller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmüller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmüller spaces and provides many references to the vast literature on Teichmüller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings
Conformal structure and algebraic structure by
Irwin Kra(
)
2 editions published between 1966 and 1976 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1966 and 1976 in English and held by 2 WorldCat member libraries worldwide
Accessory parameters for punctured spheres by
Irwin Kra(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
Cusp forms associated to rank 2 parabolic subgroups of Kleinian groups by
Irwin Kra(
Book
)
2 editions published between 1989 and 1990 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1989 and 1990 in English and held by 2 WorldCat member libraries worldwide
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Audience Level
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Kids  General  Special 
Related Identities
 Bers, Lipman Other Honoree Author Editor
 Farkas, Hershel M. Author
 Rodríguez, Rubí E. 1953 Author Editor
 Gilman, Jane 1945 Author
 Maskit, Bernard Contributor Editor
 Pogorelov, A. V. (Alekseĭ Vasilʹevich) 19192002 Author
 Zaustinskiy, Eugene
 American Mathematical Society Other Publisher
 Krushkalʹ, S. L. (Samuil Leĭbovich) Author
 American Mathematical Society Meeting (1974 : San Francisco, Calif.)
Useful Links
Associated Subjects
Automorphic functions Banach algebras Banach spaces Bers, Lipman Conformal mapping Differential equations, Partial Functional analysis Functions Functions, Theta Functions of complex variables Geometric function theory Geometry, Algebraic GeometryFoundations Global analysis (Mathematics) Group theory Holomorphic functions Kleinian groups Mappings (Mathematics) Mathematical analysis Mathematicians Mathematics Modular groups Quasiconformal mappings Riemann surfaces Rings (Algebra) Teichmüller spaces Topological groups United States
Alternative Names
Irwin Kra American mathematician
Irwin Kra Amerikaans wiskundige
Irwin Kra amerikansk matematikar
Irwin Kra amerikansk matematiker
Irwin Kra matemático estadounidense
Irwin Kra USamerikanischer Mathematiker
Kra, I.
Kra, I. 1937
Kra, Irvin
Kra, Irvin 1937
Kra, Irwin
Kra, Irwin 1937
Кра, И..
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