An Isaac Newton Institute Workshop

Matrix Ensembles and L-Functions

Zeros of random polynomials and linear combinations of random characteristic polynomials

15th July 2004

Author: Ashkan Nikeghbali (Université Paris VI, Jussieu)

Abstract

In this talk, we shall give results about the asymptotic behavior of roots of random polynomials in the plane. We then specialize to the case of sums of characteristic polynomials of random unitary matrices: we prove an analogue of a result by Bombieri and Hejhal about the zeros on the critical line for linear combination of L-functions.