Karat︠s︡uba, Anatoliĭ Alekseevich
Overview
Works:  26 works in 107 publications in 4 languages and 2,116 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA246.8.T75, 512.7 
Publication Timeline
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Most widely held works by
Anatoliĭ Alekseevich Karat︠s︡uba
Trigonometric sums in number theory and analysis
by
Gennadiĭ Ivanovich Arkhipov(
)
11 editions published between 2004 and 2008 in English and held by 902 WorldCat member libraries worldwide
The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I.M. Vinogradov's estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and present purely arithmetic results concerning the solvability of equations in integers
11 editions published between 2004 and 2008 in English and held by 902 WorldCat member libraries worldwide
The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I.M. Vinogradov's estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and present purely arithmetic results concerning the solvability of equations in integers
Complex analysis in number theory
by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
9 editions published in 1995 in English and held by 270 WorldCat member libraries worldwide
9 editions published in 1995 in English and held by 270 WorldCat member libraries worldwide
The Riemann zetafunction
by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
11 editions published in 1992 in English and held by 226 WorldCat member libraries worldwide
The Riemann ZetaFunction (De Gruyter Expositions in Mathematics)
11 editions published in 1992 in English and held by 226 WorldCat member libraries worldwide
The Riemann ZetaFunction (De Gruyter Expositions in Mathematics)
Basic analytic number theory
by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
11 editions published between 1983 and 1993 in English and Undetermined and held by 217 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
11 editions published between 1983 and 1993 in English and Undetermined and held by 217 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
)
9 editions published between 1980 and 1982 in 3 languages and held by 179 WorldCat member libraries worldwide
9 editions published between 1980 and 1982 in 3 languages and held by 179 WorldCat member libraries worldwide
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 International Conference on Number Theory(
Book
)
8 editions published in 1995 in English and held by 128 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"T.p. verso
8 editions published in 1995 in English and held by 128 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"T.p. verso
Analytic number theory and applications : collected papers in honor of sixtieth birthday of Professor Anatolii Alexeevich Karatsuba
by
O. B Lupanov(
Book
)
5 editions published in 1997 in English and held by 72 WorldCat member libraries worldwide
5 editions published in 1997 in English and held by 72 WorldCat member libraries worldwide
Osnovy analiticheskoĭ teorii chisel
by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
15 editions published between 1975 and 2004 in 3 languages and held by 58 WorldCat member libraries worldwide
15 editions published between 1975 and 2004 in 3 languages and held by 58 WorldCat member libraries worldwide
Teorii︠a︡ kratnykh trigonometricheskikh summ
by
Gennadiĭ Ivanovich Arkhipov(
Book
)
6 editions published in 1987 in Russian and held by 23 WorldCat member libraries worldwide
6 editions published in 1987 in Russian and held by 23 WorldCat member libraries worldwide
Selected works : prepared by the Steklov Mathematical Institute of the Academy of Sciences of the USSR on the occasion of his ninetieth birthday
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
Fundamentos de la teoría analítica de los números
by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
5 editions published in 1979 in Spanish and held by 6 WorldCat member libraries worldwide
5 editions published in 1979 in Spanish and held by 6 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
)
1 edition published in 2012 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 5 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
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
Primzahlverteilung
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
Teorija kratnych trigonometričeskich summ
by
Gennadiĭ Ivanovich Arkhipov(
Book
)
1 edition published in 1987 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in Russian and held by 2 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 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Theory of numbers, mathematical analysis, and their applications
by
N. N Bogoli︠u︡bov(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
Metod HardiLittlvuda
by
Robert C Vaughan(
Book
)
1 edition published in 1985 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1985 in Russian and held by 1 WorldCat member library worldwide
Number theory and analysis : proceedings of the international conference, celebrating the one hundreth anniversary of the birth of academician I. M. Vinogradov : collection of papers
by
Anatoliĭ Alekseevich Karat︠s︡uba(
Book
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Arkhipov, Gennadiĭ Ivanovich Author
 Chubarikov, Vladimir Nikolaevich Editor
 Voronin, S. M. (Sergeĭ Mikhaĭlovich) 1946
 Vinogradov, I. M. (Ivan Matveevich) 18911983 Honoree Author
 Blagodatskikh, V. I. Editor
 Mischenko, E. F. (Evgeniĭ Frolovich)
 Koblitz, Neal Translator
 Mardzhanishvili, K. K. Editor
 Mishchenko, E. F. (Evgeniĭ Frolovich) Editor
 Parshin, A. N.
Useful Links
Alternative Names
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
Карацуба, Анатолий Алексеевич
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