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"Low-lying zeros of Dedekind zeta functions" February 07, 2011 (10:00 AM PST - 10:50 AM PST)
Parent Program: --
Location: SLMath: Eisenbud Auditorium
Speaker(s) Andrew Yang
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

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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