Van der Corput's Method of Exponential Sums

This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums.

S. W. Graham (Author), Grigori Kolesnik (Author)

9780521339278, Cambridge University Press

Paperback, published 25 January 1991

132 pages
22.7 x 15.2 x 0.9 cm, 0.196 kg

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.

1. Introduction
2. The simplest Van Der Corput estimates
3. The method of exponent pairs
4. Application of exponent pairs
5. Computing optimal exponent pairs
6. Two dimensional exponential sums
7. New exponent pairs.

Subject Areas: Number theory [PBH]