EVENT DETAILS AND ABSTRACT

Title: Families of automorphic L-functions
Speaker: Sug Woo Shin
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

Automorphic L-functions generalize the Riemann zeta function, Dirichlet L-functions and the L- functions associated to modular forms. Analytic questions involving a single L-function, such as the location of its zeros, are arithmetically significant but elusive to study. One way to overcome the difficulty is to study L-functions in families. Katz and Sarnak studied the distribution of the low-lying zeros in a family of L-functions and predicted that they follow some specific models in random matrix theory. (Low-lying zeros roughly refer to the zeros of L-functions on the line Re(s) = 1/2 with small imaginary part). I will present my result (joint with Nicolas Templier) which confirms their prediction for a good number of cases and suggests a general recipe, not known before, to predict the random matrix model for a given family.