Urbana Campus Research Calendar (OVCRI)

View Full Calendar

Number Theory Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Altgeld Hall 145
Date
Sep 23, 2025   11:00 - 11:50 am  
Speaker
Asif Zaman (University of Toronto)
Contact
Yuan Liu
E-Mail
yyyliu@illinois.edu
Views
25
Originating Calendar
Number Theory Seminar Calendar

Title:   Effective Brauer-Siegel theorems for Artin L-functions

Abstract:   Given a number field K (other than Q), in a now classic work, Stark pinpointed the possible source of a so-called Landau--Siegel zero of the Dedekind zeta function ζ_K(s) and used this to give effective upper and lower bounds on the residue of ζ_K(s) at s=1.  I will discuss an extension of Stark's work to give effective upper and lower bounds for the leading term of the Laurent expansion of general Artin L-functions at s=1 that are, up to the value of implied constants, as strong as could reasonably be expected given current progress toward the generalized Riemann hypothesis.  The bounds are completely unconditional, and rely on no unproven hypotheses about Artin L-functions.  This is joint work with Peter Cho and Robert Lemke Oliver.

link for robots only