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Other titles in the Cambridge Tracts in Mathematics series:
Cambridge Tracts in Mathematics #0127: Spectral Theory of the Riemann Zeta-Functionby Y. Motohashi
Synopses & Reviews
This ground-breaking work combines the classic (the zeta-function) with the modern (the spectral theory) to create a comprehensive but elementary treatment of spectral resolution. The story starts with a basic but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. The author achieves this by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory. These ideas are then utilized to unveil a new image of the zeta-function, revealing it as 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 recent development of number theory. Mathematics specialists and researchers will find this a fascinating work.
The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book 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. It will be fascinating reading for all mathematicians working in analytic number theory or the theory of automorphic forms.
Monograph on most important topic in number theory.
Includes bibliographical references (p. 221-224) and indexes.
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