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Other titles in the Cambridge Studies in Advanced Mathematics series:
Cambridge Studies in Advanced Mathematics #14: Intro Theo Riemann Zeta Functionby Stephen J. Patterson
Synopses & Reviews
This is a modern introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function.
A modern introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function.
This modern introduction to the analytic techniques used in the investigation of zeta-function avoids technical results and the customary function-theoretic approach. Since Riemann's introduction, many other classes of "zeta-function" have been introduced and are now intensively studied.
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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