Description

Book Synopsis
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 develo

Trade Review
Review 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 theorists.' R. Tichy, International Mathematical News

Table of Contents
1. Non-Euclidean harmonics; 2. Trace formulas; 3. Automorphic L-functions; 4. An explicit formula; 5. Asymptotics; References; Index.

Spectral Theory of the Riemann ZetaFunction 127 Cambridge Tracts in Mathematics Series Number 127

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    A Hardback by Yoichi Motohashi

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      View other formats and editions of Spectral Theory of the Riemann ZetaFunction 127 Cambridge Tracts in Mathematics Series Number 127 by Yoichi Motohashi

      Book details

      Publisher Cambridge University Press
      Published 9 November 1997
      ISBN-13 9780521445207
      978-0521445207
      ISBN-10 0521445205
      Also in:
      Complex analysis, complex variables

      Description

      Book Synopsis
      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 develo

      Trade Review
      Review 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 theorists.' R. Tichy, International Mathematical News

      Table of Contents
      1. Non-Euclidean harmonics; 2. Trace formulas; 3. Automorphic L-functions; 4. An explicit formula; 5. Asymptotics; References; Index.

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