Speaker: Ofir Gorodetsky
(Tel-Aviv University):
Title:
Explicit formulas for the numbers of prime polynomials in short intervals

Abstract:
Gauss was the first to determine the number of prime polynomials in F_q[T] of degree n, establishing the Prime Polynomial Theorem. A natural extension of this problem is to count prime polynomials with first L coefficients prescribed. We describe the values of q and L for which it is possible to give a closed form formula for this counting question, by relating it to supersingularity of certain curves. This extends works of Carlitz and Kuzmin.