Analytic Number Theory

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Cambridge University Press, Oct 16, 1997 - Mathematics - 382 pages
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This volume presents an authoritative, up-to-date review of analytic number theory. It contains outstanding contributions from leading international figures in this field. Core topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach conjecture, and diophantine approximations and equations. This will be a valuable book for graduates and researchers working in number theory.
 

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Contents

1 Subvarieties of Linear Tori and the Unit Equation A Survey
1
2 Remarks on the Analytic Complexity of Zeta Functions
21
3 Normal Distribution of Zeta Functions and Applications
31
4 Goldbach Numbers and Uniform Distribution
43
5 The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number ...
53
6 The BrunTitchmarsh Theorem
85
7 A Decomposition of Riemanns ZetaFunction
95
8 Multiplicative Properties of Consecutive Integers
103
14 The Goldbach Problem with Primes in Arithmetic Progressions
227
15 On the Sum of Three Squares of Primes
253
16 Trace Formula over the Hyperbolic Upper Half Space
265
17 Modular Forms and the Chebotarev Density Theorem II
287
18 Congruences between Modular Forms
309
19 Regular Singularities in GFunction Theory
321
20 Spectral Theory and Lfunctions
337
21 Irrationality Criteria for Numbers of Mahlers Type
343

9 On the Equation xm lx 1 yq with x Power
119
10 Congruence Families of Exponential Sums
127
11 On Some Results Concerning the Riemann Hypothesis
139
12 Mean Values of Dirichlet Series via Laplace Transforms
169
13 The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem ...
209
22 Hypergeometric Functions and Irrationality Measures
353
23 Forms in Many Variables
361
24 Remark on the Kuznetsov Trace Formula
377
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About the author (1997)

Motohashi-Nihon University, Tokyo

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