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.
Author(s): Yoichi Motohashi
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1997
Language: English
Pages: 393
Cover......Page 1
London Mathematical Society Lecture Note Series 247......Page 2
Analytic Number Theory......Page 4
9780521625128......Page 5
Contents......Page 6
Foreword......Page 8
Speakers......Page 10
Subvarieties of Linear Tori and the Unit Equation: A Survey......Page 12
Remarks on the Analytic Complexity of Zeta Functions......Page 32
Normal Distribution of Zeta Functions and Applications......Page 42
Goldbach Numbers and Uniform Distribution mod 1......Page 54
The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number......Page 64
The Brun-Titchmarsh Theorem......Page 96
A Decomposition of Riemann's Zeta-Function......Page 106
Multiplicative Properties of Consecutive Integers......Page 114
On the Equation (x^m - 1)/(x - 1) = y^q with x Power......Page 130
Congruence Families of Exponential Sums......Page 138
On Some Results Concerning the Riemann Hypothesis......Page 150
Mean Values of Dirichlet Series via Laplace Transforms......Page 180
The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem......Page 220
The Goldbach Problem with Primes in Arithmetic Progressions......Page 238
On the Sum of Three Squares of Primes......Page 264
Trace Formula over the Hyperbolic Upper Half Space......Page 276
Modular Forms and the Chebotarev Density Theorem, II......Page 298
Congruences between Modular Forms......Page 320
Regular Singularities in G-Function Theory......Page 332
Spectral Theory and L-functions, Talk Report......Page 348
Irrationality Criteria for Numbers of Mahler's Type......Page 354
Hypergeometric Functions and Irrationality Measures......Page 364
Forms in Many Variables......Page 372
Remark on the Kuznetsov Trace Formula......Page 388
