Book contents
- Frontmatter
- Contents
- Foreword
- Speakers
- 1 Subvarieties of Linear Tori and the Unit Equation A Survey
- 2 Remarks on the Analytic Complexity of Zeta Functions
- 3 Normal Distribution of Zeta Functions and Applications
- 4 Goldbach Numbers and Uniform Distribution
- 5 The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number
- 6 The Brun–Titchmarsh Theorem
- 7 A Decomposition of Riemann's Zeta-Function
- 8 Multiplicative Properties of Consecutive Integers
- 9 On the Equation (xm – 1)/(x – 1) = yq with x Power
- 10 Congruence Families of Exponential Sums
- 11 On Some Results Concerning the Riemann Hypothesis
- 12 Mean Values of Dirichlet Series via Laplace Transforms
- 13 The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem
- 14 The Goldbach Problem with Primes in Arithmetic Progressions
- 15 On the Sum of Three Squares of Primes
- 16 Trace Formula over the Hyperbolic Upper Half Space
- 17 Modular Forms and the Chebotarev Density Theorem II
- 18 Congruences between Modular Forms
- 19 Regular Singularities in G-Function Theory
- 20 Spectral Theory and L-functions
- 21 Irrationality Criteria for Numbers of Mahler's Type
- 22 Hypergeometric Functions and Irrationality Measures
- 23 Forms in Many Variables
- 24 Remark on the Kuznetsov Trace Formula
Foreword
Published online by Cambridge University Press: 08 April 2010
- Frontmatter
- Contents
- Foreword
- Speakers
- 1 Subvarieties of Linear Tori and the Unit Equation A Survey
- 2 Remarks on the Analytic Complexity of Zeta Functions
- 3 Normal Distribution of Zeta Functions and Applications
- 4 Goldbach Numbers and Uniform Distribution
- 5 The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number
- 6 The Brun–Titchmarsh Theorem
- 7 A Decomposition of Riemann's Zeta-Function
- 8 Multiplicative Properties of Consecutive Integers
- 9 On the Equation (xm – 1)/(x – 1) = yq with x Power
- 10 Congruence Families of Exponential Sums
- 11 On Some Results Concerning the Riemann Hypothesis
- 12 Mean Values of Dirichlet Series via Laplace Transforms
- 13 The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem
- 14 The Goldbach Problem with Primes in Arithmetic Progressions
- 15 On the Sum of Three Squares of Primes
- 16 Trace Formula over the Hyperbolic Upper Half Space
- 17 Modular Forms and the Chebotarev Density Theorem II
- 18 Congruences between Modular Forms
- 19 Regular Singularities in G-Function Theory
- 20 Spectral Theory and L-functions
- 21 Irrationality Criteria for Numbers of Mahler's Type
- 22 Hypergeometric Functions and Irrationality Measures
- 23 Forms in Many Variables
- 24 Remark on the Kuznetsov Trace Formula
Summary
This volume is an outcome of
The 39th Taniguchi International Symposium on Mathematics
Analytic Number Theory
May 13–17, 1996, Kyoto
organized by myself, and of its forum, May 20–24, organized by N. Hirata-Kohno, L. Murata and myself as a conference at the Research Institute for Mathematical Sciences, Kyoto University.
I am deeply indebted to the Taniguchi Foundation for the generous support that made the symposium and the conference possible. The organizers of the conference acknowledge sincerely that the speakers were supported in part by the Inoue Science Foundation, the Kurata Foundation, Saneyoshi Scholarship Foundation, the Sumitomo Foundation; College of Science and Technology of Nihon University, the Research Institute for Mathematical Sciences of Kyoto University; and the Grant-Aid for General Scientific Research from the Ministry of Education, Science and Culture (through the courtesy of Prof. M. Koike, Kyushu University).
My special thanks are due to Profs. Hirata-Kohno and Murata for their unfailing collaboration during the three years of difficult preparation for the meetings.
- Type
- Chapter
- Information
- Analytic Number Theory , pp. vii - viiiPublisher: Cambridge University PressPrint publication year: 1997