Van der Corput's Method of Exponential Sums

S. W. Graham; Grigori Kolesnik

doi:10.1017/CBO9780511661976

This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem.

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Van der Corput's Method of Exponential Sums

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Acknowledgement
pp vii-viii

1 - Introduction
pp 1-5

2 - The Simplest Van Der Corput Estimates
pp 6-20

3 - The Method of Exponent Pairs
pp 21-37

4 - Applications of Exponent Pairs
pp 38-53

5 - Computing Optimal Exponent Pairs
pp 54-69

6 - Two Dimensional Exponential Sums
pp 70-85

7 - New Exponent Pairs
pp 86-110

Appendix
pp 111-116

Bibliography
pp 117-119

Index
pp 120-120

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Van der Corput's Method of Exponential Sums

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