NSF Award
1101261
The PI plans to investigate a variety of problems in the<br/>analytic theory of automorphic forms, especially problems<br/>concerning higher rank groups such as the general linear<br/>group of degree 3 and higher. In particular, the PI will<br/>study some problems concerning the analytic study of<br/>automorphic forms restricted to small subsets, especially<br/>period integrals. Other components of the research include <br/>the study of mean values of L-functions including the Riemann <br/>zeta function.<br/><br/>One of the goals of analytic number theory is to understand<br/>the statistical properties of algebraic objects. For instance,<br/>one can ask what is the probability that a randomly chosen<br/>large number is a prime. It is very fortunate for modern<br/>cryptography that it is easy to find large primes. Cryptography<br/>is a crucial tool in banking, commerce, and of course national <br/>security. Some of our best knowledge on the prime numbers<br/>comes from properties of the Riemann zeta function, the<br/>simplest L-function. Many other fascinating algebraic<br/>and geometric objects are encoded in other types of L-functions.<br/>The PI plans to study many of the statistical properties of<br/>these L-functions.
