Speaker: Andrew Yang
Abstract:  The Katz-Sarnak philosophy asserts that to any "naturally
defined family" of L-functions, there should be an associated symmetry
group which determines the distribution of the low-lying zeros (as well as
other statistics) of those L-functions.  We consider the family of
Dedekind zeta functions of cubic number fields, and we predict that the
associated symmetry group is symplectic.  There are three main
ingredients: the explicit formula, work of Davenport-Heilbronn on counting
cubic fields and the proportion of fields in which rational primes have
given splitting type, and power-saving error terms for these counts, first
obtained by Belabas-Bhargava-Pomerance.

Location: Simons Auditorium