Spectral Theory of the Riemann Zeta-Function (Cambridge Tracts in Mathematics, Book 127)
Spectral Theory of the Riemann Zeta-Function (Cambridge Tracts in Mathematics, Book 127) by Yoichi Motohashi
English | 1997 | ISBN: 0521445205 | ISBN-13: 9780521445207 | 240 pages | PDF | 7 MB
English | 1997 | ISBN: 0521445205 | ISBN-13: 9780521445207 | 240 pages | PDF | 7 MB
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.