Automorphic Forms and Distribution Laws for Discrete Subgroups

Research Foundation Of The City University Of New York (Lehman), Bronx NY

Investigators

Abstract

Abstract for award DMS-0401318 of Petridis The principal investigator will investigate the distribution of modular symbols and period polynomials (Gaussian distribution laws). He will study perturbed Eisenstein series in Teichmueller space and character varieties in relation to the disappearance of cusp forms (higher order Phillips-Sarnak conditions), and apply analytic number theory techniques in the spectral theory of Hilbert modular varieties (subconvex estimates of the L-series of a Maass cusp form and equidistribution of Eisenstein series) and Heisenberg manifolds (distribution of the error term in Weyl's law for the eigenvalues of the Laplace operator). This research falls into the general mathematical field of Number Theory. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.