WorldCat Identities

Karat︠s︡uba, Anatoliĭ Alekseevich

Overview
Works: 27 works in 123 publications in 4 languages and 2,445 library holdings
Genres: Conference papers and proceedings  Bibliography  Bio-bibliography  Biography 
Roles: Author, Editor, Honoree, Other
Classifications: QA241, 512.73
Publication Timeline
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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

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 k-th 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

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
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
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

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

Teorii︠a︡ kratnykh trigonometricheskikh summ by Gennadiĭ Ivanovich Arkhipov( Book )

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

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

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
Teorii︠a︡ chisel i analiz : trudy Mezhdunarodnoĭ konferent︠s︡ii po teorii chisel, posvi︠a︡shchennoĭ 100-letii︠u︡ 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

Raspredelenie prostych čisel by Karl Prachar( Book )

1 edition published in 1967 in Russian and held by 3 WorldCat member libraries worldwide

Dzeta-funkcija Rimana by S. M Voronin( Book )

2 editions published in 1994 in Russian and held by 3 WorldCat member libraries worldwide

Teorija čisel, algebra i analiz : sbornik statej ; k 75-letiju 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
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

Teoriia kratnyh trigonometricheskih summ by Gennadiĭ Ivanovich Arkhipov( Book )

1 edition published in 1987 in Undetermined and held by 1 WorldCat member library worldwide

Matematika i informatika : k 75-letiju so dnja roždenija Anatolija Alekseeviča Karacuby( Book )

1 edition published in 2012 in Russian and held by 1 WorldCat member library worldwide

 
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Trigonometric sums in number theory and analysis
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 (1937-2008)

Anatolij Alexejevič Karacuba

Anatolijus Karacuba

Karačuba, A.A.

Karacuba, A. A. 1937-2008

Karacuba, Anatolij A. 1937-2008

Karacuba, Anatolij Alekseevič

Karacuba, Anatolij Alekseevič 1937-2008

Karatsouba Anatoli Alekseevitch 1937-....

Karat︠s︡uba, A. A.

Karat︠s︡uba, A. A. 1937-2008

Karat︠s︡uba, A. A. (Anatoliĭ Alekseevich)

Karatsuba Anatoliĭ Alekseevich

Kara︠ts︡uba, Anatoliĭ Alekseevich 1937-2008

Karatsuba, Anatolii Alexeevich 1937-2008

Karatsuba Anatolij A.

Karatsuba, Anatolij A. 1937-2008

Karatsuba, Anatolij Alekseevich 1937-2008

Karat︠s︡uba, Anatoly A.

Karat︠s︡uba, Anatoly A. 1937-2008

Karazuba, Anatoli Alexejewitsch 1937-2008

Анатолий Алексеевич Карацуба

Анатолий Карацуба

Карацуба, Анатолий Алексеевич

Карацуба Анатолій Олексійович

آناتولی کاراتسوبا ریاضی‌دان روسی

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Languages
English (64)

Russian (34)

Spanish (6)

German (1)

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