Karat︠s︡uba, Anatoliĭ Alekseevich
Overview
Works:  27 works in 123 publications in 4 languages and 2,445 library holdings 

Genres:  Conference papers and proceedings Bibliography Biobibliography Biography 
Roles:  Author, Editor, Honoree, Other 
Classifications:  QA241, 512.73 
Publication Timeline
.
Most widely held works by
Anatoliĭ Alekseevich Karat︠s︡uba
Complex analysis in number theory by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
10 editions published in 1995 in English and Undetermined and held by 290 WorldCat member libraries worldwide
10 editions published in 1995 in English and Undetermined and held by 290 WorldCat member libraries worldwide
Basic analytic number theory by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
16 editions published between 1983 and 2013 in English and Undetermined and held by 254 WorldCat member libraries worldwide
This book provides an introduction to four central problems in analytic number theory. These are (1) the problem of estimating the number of integerpoints in planar domains (2) the problem of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions (3) Goldbach's problem on sums of primes, and (4) Waring's problem on sums of kth powers. To solve these problems, one uses the fundamental methods of analytic number theory: complex integration, I.M. Vinogradov's method of trigonometric sums, and the circle method of G.H. Hardy, J.E. Littlewood, and S. Ramanujan. There are numerous exercises at the end of each chapter. These exercises either refine the theorems proved in the text, or lead to new ideas in number theory. The author also includes a section of hints for the solution of the exercises. The mathematical prerequisites for this volume are undergraduate courses in number theroy, mathematical analysis, and complex variables. The book would be an excellent text for a one or two semester course in analytic number theory for advanced undergraduates or graduate students
16 editions published between 1983 and 2013 in English and Undetermined and held by 254 WorldCat member libraries worldwide
This book provides an introduction to four central problems in analytic number theory. These are (1) the problem of estimating the number of integerpoints in planar domains (2) the problem of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions (3) Goldbach's problem on sums of primes, and (4) Waring's problem on sums of kth powers. To solve these problems, one uses the fundamental methods of analytic number theory: complex integration, I.M. Vinogradov's method of trigonometric sums, and the circle method of G.H. Hardy, J.E. Littlewood, and S. Ramanujan. There are numerous exercises at the end of each chapter. These exercises either refine the theorems proved in the text, or lead to new ideas in number theory. The author also includes a section of hints for the solution of the exercises. The mathematical prerequisites for this volume are undergraduate courses in number theroy, mathematical analysis, and complex variables. The book would be an excellent text for a one or two semester course in analytic number theory for advanced undergraduates or graduate students
Multiple trigonometric sums by
Gennadiĭ Ivanovich Arkhipov(
Book
)
10 editions published between 1980 and 1982 in 3 languages and held by 194 WorldCat member libraries worldwide
10 editions published between 1980 and 1982 in 3 languages and held by 194 WorldCat member libraries worldwide
Trigonometric sums in number theory and analysis by
Gennadiĭ Ivanovich Arkhipov(
Book
)
13 editions published between 2004 and 2008 in English and held by 153 WorldCat member libraries worldwide
&Quot;In this book a systematic account of the theory of multiple trigonometric sums is given as created by the authors over a period of more than twenty years. The authors develop a unified approach with which they obtain estimates for these sums similar to the classical ones of I. M. Vinogradov. They use them to solve several problems in analytic number theory and investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis. Moreover, purely arithmetical results concerning the solvability of equations in integers are presented." "This book is intended for graduate students and researchers in number theory, probability theory, and analysis."BOOK JACKET
13 editions published between 2004 and 2008 in English and held by 153 WorldCat member libraries worldwide
&Quot;In this book a systematic account of the theory of multiple trigonometric sums is given as created by the authors over a period of more than twenty years. The authors develop a unified approach with which they obtain estimates for these sums similar to the classical ones of I. M. Vinogradov. They use them to solve several problems in analytic number theory and investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis. Moreover, purely arithmetical results concerning the solvability of equations in integers are presented." "This book is intended for graduate students and researchers in number theory, probability theory, and analysis."BOOK JACKET
Number theory and analysis : proceedings of the International Conference on Number Theory, celebrating the one hundredth anniversary
of the birth of Academician I.M. Vinogradov : collection of papers by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
10 editions published in 1995 in English and held by 140 WorldCat member libraries worldwide
"This collection consists of papers ... devoted to current trends in analytic number theory, function theory, algebraic number theory, algebraic geometry, and combinatorics"Title page verso
10 editions published in 1995 in English and held by 140 WorldCat member libraries worldwide
"This collection consists of papers ... devoted to current trends in analytic number theory, function theory, algebraic number theory, algebraic geometry, and combinatorics"Title page verso
Analytic number theory and applications : collected papers in honor of sixtieth birthday of Professor Anatolii Alexeevich
Karatsuba by
O. B Lupanov(
Book
)
7 editions published in 1997 in English and held by 80 WorldCat member libraries worldwide
7 editions published in 1997 in English and held by 80 WorldCat member libraries worldwide
Osnovy analiticheskoĭ teorii chisel by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
26 editions published between 1975 and 2004 in 4 languages and held by 70 WorldCat member libraries worldwide
26 editions published between 1975 and 2004 in 4 languages and held by 70 WorldCat member libraries worldwide
Teorii︠a︡ kratnykh trigonometricheskikh summ by
Gennadiĭ Ivanovich Arkhipov(
Book
)
5 editions published in 1987 in Russian and held by 22 WorldCat member libraries worldwide
5 editions published in 1987 in Russian and held by 22 WorldCat member libraries worldwide
Teorija kratnych trigonometričeskich summ by
Gennadiĭ Ivanovich Arkhipov(
Book
)
2 editions published in 1987 in Russian and held by 11 WorldCat member libraries worldwide
2 editions published in 1987 in Russian and held by 11 WorldCat member libraries worldwide
Number theory, algebra, and analysis : collected papers dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion
of his 75th birthday(
Book
)
3 editions published in 2012 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 2012 in English and held by 9 WorldCat member libraries worldwide
Selected works by
I. M Vinogradov(
Book
)
2 editions published in 2014 in English and held by 6 WorldCat member libraries worldwide
I.M. Vinogradov (1891  1983) was one of the creators of modern analytic number theory. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for five years during World War II. This edition includes a selection of articles, chosen by the author himself, which highlight the important stages of his scientific career. In addition to some early works, it contains the initial proofs of many of Vinogradov's basic theorems as well as the later improved versions, and also two substantial monographs
2 editions published in 2014 in English and held by 6 WorldCat member libraries worldwide
I.M. Vinogradov (1891  1983) was one of the creators of modern analytic number theory. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for five years during World War II. This edition includes a selection of articles, chosen by the author himself, which highlight the important stages of his scientific career. In addition to some early works, it contains the initial proofs of many of Vinogradov's basic theorems as well as the later improved versions, and also two substantial monographs
Analiticheskai︠a︡ teorii︠a︡ chisel i prilozhenii︠a︡ : sbornik stateĭ : k 60letii︠u︡ so dni︠a︡ rozhdenii︠a︡ professora Anatolii︠a︡
Alekseevicha Karat︠s︡uby(
Book
)
1 edition published in 1997 in Russian and held by 4 WorldCat member libraries worldwide
1 edition published in 1997 in Russian and held by 4 WorldCat member libraries worldwide
Teorii︠a︡ chisel i analiz : trudy Mezhdunarodnoĭ konferent︠s︡ii po teorii chisel, posvi︠a︡shchennoĭ 100letii︠u︡ so dni︠a︡
rozhdenii︠a︡ I.M. Vinogradova : sbornik stateĭ by International Conference on Number Theory(
Book
)
1 edition published in 1994 in Russian and held by 4 WorldCat member libraries worldwide
1 edition published in 1994 in Russian and held by 4 WorldCat member libraries worldwide
Raspredelenie prostych čisel by
Karl Prachar(
Book
)
1 edition published in 1967 in Russian and held by 3 WorldCat member libraries worldwide
1 edition published in 1967 in Russian and held by 3 WorldCat member libraries worldwide
Number theory algebra mathematical analysis and their applications : dedicated to the 100th anniversary of the birth of ivan
matveevich vinogradov : collection of papers(
Book
)
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
Dzetafunkcija Rimana by
S. M Voronin(
Book
)
2 editions published in 1994 in Russian and held by 3 WorldCat member libraries worldwide
2 editions published in 1994 in Russian and held by 3 WorldCat member libraries worldwide
Teorija čisel, algebra i analiz : sbornik statej ; k 75letiju so dnja roždenija professora Anatolija Alekseeviča Karacuby(
Book
)
1 edition published in 2012 in Russian and held by 2 WorldCat member libraries worldwide
This volume is dedicated to the memory of the outstanding scientist Anatolii Alekseevich Karatsuba. The volume contains papers dealing with a wide range of topics in analytic number theory and related fields of algebra and analysis. The volume will be of interest to specialists, postgraduates, and senior students of mathematical specialties
1 edition published in 2012 in Russian and held by 2 WorldCat member libraries worldwide
This volume is dedicated to the memory of the outstanding scientist Anatolii Alekseevich Karatsuba. The volume contains papers dealing with a wide range of topics in analytic number theory and related fields of algebra and analysis. The volume will be of interest to specialists, postgraduates, and senior students of mathematical specialties
Ivan Matveevich Vinogradov by
T. B Jarina(
Book
)
3 editions published in 1978 in Russian and Undetermined and held by 2 WorldCat member libraries worldwide
3 editions published in 1978 in Russian and Undetermined and held by 2 WorldCat member libraries worldwide
Teoriia kratnyh trigonometricheskih summ by
Gennadiĭ Ivanovich Arkhipov(
Book
)
1 edition published in 1987 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1987 in Undetermined and held by 1 WorldCat member library worldwide
Matematika i informatika : k 75letiju so dnja roždenija Anatolija Alekseeviča Karacuby(
Book
)
1 edition published in 2012 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 2012 in Russian and held by 1 WorldCat member library worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Chubarikov, Vladimir Nikolaevich Editor
 Arkhipov, Gennadiĭ Ivanovich Author
 Vinogradov, I. M. (Ivan Matveevich) 18911983 Honoree Author
 Blagodatskikh, V. I. Editor
 Mischenko, E. F. (Evgeniĭ Frolovich) Editor
 Parshin, A. N.
 Nathanson, Melvyn B. Translator
 Mardzhanishvili, K. K. Editor
 International Conference on Number Theory (1991, Moskva)
 Faddeev, L. D. Editor
Useful Links
Alternative Names
Anatoli Alexejewitsch Karazuba sowjetischer bzw. russischer Mathematiker
Anatoli Karatsuba
Anatolii Alexeevitch Karatsuba Russian mathematician
Anatolii Alexeievitch Karatsuba
Anatolii Alexevich Karatsuba
Anatolij Alekseevič Karacuba
Anatolij Alekseevič Karacuba matematico russo
Anatolij Alekseevič Karacuba Russisch wiskundige (19372008)
Anatolij Alexejevič Karacuba
Anatolijus Karacuba
Karačuba, A.A.
Karacuba, A. A. 19372008
Karacuba, Anatolij A. 19372008
Karacuba, Anatolij Alekseevič
Karacuba, Anatolij Alekseevič 19372008
Karatsouba Anatoli Alekseevitch 1937....
Karat︠s︡uba, A. A.
Karat︠s︡uba, A. A. 19372008
Karat︠s︡uba, A. A. (Anatoliĭ Alekseevich)
Karatsuba Anatoliĭ Alekseevich
Kara︠ts︡uba, Anatoliĭ Alekseevich 19372008
Karatsuba, Anatolii Alexeevich 19372008
Karatsuba Anatolij A.
Karatsuba, Anatolij A. 19372008
Karatsuba, Anatolij Alekseevich 19372008
Karat︠s︡uba, Anatoly A.
Karat︠s︡uba, Anatoly A. 19372008
Karazuba, Anatoli Alexejewitsch 19372008
Анатолий Алексеевич Карацуба
Анатолий Карацуба
Карацуба, Анатолий Алексеевич
Карацуба Анатолій Олексійович
آناتولی کاراتسوبا ریاضیدان روسی
アナトリー・カラツバ
Languages
Covers