NSF Award
0502730
This project explores the relationship between moments of the Riemann zeta <br/>function and automorphic forms. Motivated by recent conjectures on the <br/>moments, Professor Beineke plans to continue development of a new class <br/>of automorphic summation formulae in order to establish connections <br/>between the 2k-th moment of the Riemann zeta function and Eisenstein <br/>series on GL(2k). Initial results in the case where k = 1 have been developed <br/>by Professor Beineke in collaboration with Professor Daniel Bump at <br/>Stanford University.<br/><br/>This is a project in number theory, one of the oldest branches of <br/>mathematics. The foundations of number theory lie in the study of the <br/>positive integers and finding patterns in these integers. A function of <br/>interest in number theory, which may provide information about patterns <br/>of prime numbers, is the Riemann zeta function. Results about this function <br/>could have applications to cryptography and Internet security. Professor <br/>Beineke's project investigates other number-theoretic objects called <br/>automorphic forms, and their possible connections to average values of <br/>the Riemann zeta function. These connections were initially motivated by <br/>results stemming from Random Matrix Theory, a subject originally <br/>used to develop models in experimental physics.
