An introduction to the theory of the Riemann zeta-function
Author(s)
Bibliographic Information
An introduction to the theory of the Riemann zeta-function
(Cambridge studies in advanced mathematics, 14)
Cambridge University Press, 1995
- : pbk
Available at 32 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library & Science Information Center, Osaka Prefecture University
: pbk3000051647,
pbk20400073568
Note
"First published 1988. Reprinted 1989. First paperback edtion 1995"--T.p. verso
Bibliography: p. [152]-154
Includes index
Description and Table of Contents
Description
This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann 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 emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.
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 Lindeloef 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.
by "Nielsen BookData"