Spectral theory of the Riemann zeta-function

Includes index

Includes bibliography (p. 221-224) and references

Convention and assumed background 1. Non-Euclidean harmonics 2. Trace formulas 3. Automorphic L-functions 4. An explicit formula 5. Asymptotics.

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.