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Spectral Theory of the Riemann Zeta-Function

By: Yoichi Motohashi

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Paperback | 15 May 2008

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240 Pages

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22.8 x 15.3 x 1.5

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The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.

Industry Reviews

From reviews of the hardback: '... gives an excellent presentation of the interplay between the Riemann zeta function and automorphic forms ... nicely written and of great interest for any number theoriest.' R. Tichy, International Mathematical News

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Number Theory Complex Analysis Algebra

Non-Euclidean harmonics
Trace formulas
Automorphic L-functions
An explicit formula
Asymptotics
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Spectral Theory of the Riemann Zeta-Function

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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