Families of L-functions and Applications

Princeton University, Princeton NJ

Investigators

Abstract

The investigator will continue his study of L-functions. Specifically the problem of a 'subconvex' estimate for general automorphic L-functions. These have wide applications to classical problems in number theory (e.g. Hilbert's 11-th problem on representing integers in a number field by a quadratic form) and to eigenfunctions on arithmetic surfaces. The use of the families of L-functions and symmetries associated with them is crucial. This project is concerned with the study of mathematical objects called zeta functions. They encode deep information about the arithmetic and geometry which lie at their definition. Understanding the functions has far reaching applications to the theory of whole numbers (and prime numbers) and more surprisingly to some foundational problems in quantum theory.