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Basic analytic number theory

Basic analytic number theory (1회 대출)

자료유형
단행본
개인저자
Karatsuba, Anatoli? Alekseevich.
서명 / 저자사항
Basic analytic number theory / Anatolij A. Karatsuba ; translated from the Russian by Melvyn B. Nathanson.
발행사항
Berlin ;   New York :   Springer-Verlag ,   c1993.  
형태사항
xiii, 222 p. : ill. ; 24 cm.
ISBN
3540533451 (Berlin : alk. paper) 0387533451 (New York : alk. paper)
일반주기
Translation of: Osnovy analitichesko? teorii chisel.  
서지주기
Includes bibliographical references (p. [219]) and index.
일반주제명
Number theory.
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008 911028s1993 nyua b 00110 eng
010 ▼a 91040715
020 ▼a 3540533451 (Berlin : alk. paper)
020 ▼a 0387533451 (New York : alk. paper)
040 ▼a DLC ▼c DLC ▼d DLC
041 1 ▼a eng ▼h rus
050 0 0 ▼a QA241 ▼b .K3313 1993
082 0 0 ▼a 512/.73 ▼2 20
090 ▼a 512.73 ▼b K18bE
100 1 0 ▼a Karatsuba, Anatoli? Alekseevich.
240 1 0 ▼a Osnovy analitichesko? teorii chisel. ▼l English
245 1 0 ▼a Basic analytic number theory / ▼c Anatolij A. Karatsuba ; translated from the Russian by Melvyn B. Nathanson.
260 0 ▼a Berlin ; ▼a New York : ▼b Springer-Verlag , ▼c c1993.
300 ▼a xiii, 222 p. : ▼b ill. ; ▼c 24 cm.
500 ▼a Translation of: Osnovy analitichesko? teorii chisel.
504 ▼a Includes bibliographical references (p. [219]) and index.
650 0 ▼a Number theory.

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고7층/ 청구기호 512.73 K18bE 등록번호 111023239 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차


CONTENTS
Translatoes Preface = ⅷ
Introductibn to theEnAlish Editloh = ⅸ
Introduction to ihe'geond Russian 1dltion = ⅹ
Notation = xii
Chapter Ⅰ. Integer Points = 1
 1. Statement of the Problem, Auxiliary Remarks, and the Simplest Results = 1
 2. The Connection Between Problems in the Theory of Integer Points and Trigonometric Sums = 6
 3. Theorems on Trigonometric Sums = 10
 4. Integer Points in a Circle and Under a Hyperbola = 21
 Exercises = 25
Chapter Ⅱ. Entire Functions of Finite Order = 27
 1. Infinite Products. Weierstrass's Formula = 27
 2. Entire Functions of Finite Order = 32
 Exercises = 38
Chapter Ⅲ. The Euler Gamma Function = 41
 1. Definition and Simplest Properties = 41
 2. Stirling's Formula = 44
 3. The Euler Beta Function and Dirichlet's Integral = 45
 Exercises = 48
Chapter Ⅳ. The Riemann Zeta Function = 51
 1. Definition and Simplest Properties = 51
 2. Simplest Theorems on the Zeros = 56
 3. Approximation by a Finite Sum = 61
 Exercises = 62
Chapter Ⅴ. The Connection Between the Sum of the Coefficients of a Dirichiet Series and the Function Defined by this Series = 64
 1. A General Theorem = 64
 2. The Prime Number Theorem = 66
 3. Representation of the Chebyshev Functions as Sums Over the Zeros of the Zeta Function = 69
 Exercises = 70
Chapter Ⅵ. The Method of I.M. Vinogradov in the Theory of the Zeta Function = 73
 1. Theorem on the Mean Value of the Modulus of a Trigonometric Sum = 73
 2. Estimate of a Zeta Sum = 82
 3. Estimate for the Zeta Function Close to the Line 1 = 86
 4. A Function-Theoretic Lemma = 87
 5. A New Boundary for the Zeros of the Zeta Function = 88
 6. A New Remainder Term in the Prime, Number Theorem = 90
 Exercises = 91
Chapter Ⅶ. The Density of the Zeros of the Zeta Function and the Problem of the Distribution of Prime Numbers in Short Intervals = 94
 1. The Simplest Density Theorem = 94
 2. Prime Numbers in Short Intervals = 98
 Exercises = 100
Chapter Ⅷ. Dirichlet L-Functions = 102
 1. Characters and their Properties = 102
 2. Definition of L-Functions and their Simplest Properties = 110
 3. The Functional Equation = 113
 4. Non-trivial Zeros: Expansion of the Logarithmic Derivative as a Series in the Zero = 116
 5. Simplest Theorems on the Zeros = 117
 Exercises = 119
Chapter Ⅸ. Prime Numbers in Arithmetic Progressions = 122
 1. An Explicit Formula = 122
 2. Theorems on the Boundary of the Zeros = 124
 3. The Prime Number Theorem for Arithmetic Progressions = 135
 Exercises = 138
Chapter Ⅹ. The Goldbach Conjecture = 141
 1. Auxiliary Statements = 141
 2. The Circle Method for Goldbach's Problem = 142
 3. Linear Trigonometric Sums with Prime Numbers = 149
 4. An Effective Theorem = 153
 Exercises = 158
Chapter XI. Waring's Problem = 160
 1. The Circle Method for Waring's Problem = 160
 2. An Estimate for Weyl Sums and the Asymptotic Formula for Waring's Problem = 171
 3. An Estimate for G(n) = 174
 Exercises = 177
Hints for the Solution of the Exercises = 181
Table of Prime Numbers 4070 and their Smallest Primitive Roots = 217
Bibliography = 219
Subject Index = 221


관련분야 신착자료

Aluffi, Paolo (2021)