Van der Corputʼs 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. 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 professional...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York :
Cambridge University Press,
1991.
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| Series: | London Mathematical Society lecture note series ;
126. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Basic Definitions; 1.2 Historical Overview; 1.3 Two Dimensional Sums; 1.4 The method of Bombieri and Iwaniec; 1.5 Notation; 2 The Simplest Van Der Corput Estimates; 2.1 Estimates Using First and Second Derivatives; 2.2 Some Simple Inequalities; 2.3 The Weyl-van der Corput Inequality; 2.4 Iterating Weyl-Van der Corput; 2.5 Upper Bounds for the Riemann Zeta-function; 2.6 Notes; 3 The Method of Exponent Pairs; 3.1 Introduction; 3.2 Lemmas on Exponential Integrals; 3.3 Heuristic Arguments and Definitions; 3.4 Proof of the A-Process
- 7.2 Preliminaries7.3 The Airy-Hardy Integral; 7.4 Gauss Sums; 7.5 Lemmas on Rational Points; 7.6 Semicubical Powers of Integers; 7.7 Proof of the Theorem; 7.8 Notes; Appendix; Bibliography; Index
