An Introduction to the Theory of the Riemann Zeta-Function

An Introduction to the Theory of the Riemann Zeta-Function

by S. J. Patterson
     
 

ISBN-10: 0521499054

ISBN-13: 9780521499057

Pub. Date: 07/28/1995

Publisher: Cambridge University Press

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory. Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively…  See more details below

Overview

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory. Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasized central ideas of broad application, avoiding technical results and the customary function-theoretic approach.

Product Details

ISBN-13:
9780521499057
Publisher:
Cambridge University Press
Publication date:
07/28/1995
Series:
Cambridge Studies in Advanced Mathematics Series, #14
Edition description:
New Edition
Pages:
172
Product dimensions:
5.98(w) x 8.98(h) x 0.39(d)

Table of Contents

1. Historical introduction; 2. The Poisson summation formula and the functional equation; 3. The Hadamard product formula and 'explicit formulae' of prime number theory; 4. The zeros of the zeta function and the prime number theorem; 5. The Riemann hypothesis and the Lindelöf hypothesis; 6. The approximate functional equation; Appendix 1. Fourier theory; 2. The Mellin transform; 3. An estimate for certain integrals; 4. The gamma function; 5. Integral functions of finite order; 6. Borel–Caratheodory theorems; 7. Littlewood's theorem.

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