Spectral Theory of the Riemann Zeta-FunctionY. MotohashiThis 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. Contents: 1. Non-Euclidean harmonics/ 2. Trace formulas/ 3. Automorphic L-functions/ 4. An explicit formula/ 5. Asymptotics/ References/ Index Series Name: Cambridge Tracts in Mathematics
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