Mathematics Colloquium - Professor Yitang Zhang

Speaker: 
Professor Yitang Zhang, University of New Hampshire
Topic: 
"On the Effective Lower Bound for $L(1,\chi)$"

ABSTRACT. Let χ be a real primitive character modulo D and L(s,χ) the Dirichlet L-function defined by

\[L(s,\chi)=\sum^{\infty}_{n=1}\frac{\chi(n)}{n^{s}}\]

for Re(s)>1. After analytic continuation, L(s,χ) is an entire function and does not vanish for Re(s)≥1. In this colloquium talk, the speaker will first survey the history of Dirichlet L-functions, the Generalized Riemann Hypothesis, zero-free regions, the hypothetically non-existent Landau-Siegel zero, and its relation with effective lower bounds for L(1,χ). Then he will describe a method that might lead to a proof of the effective lower bound

\[L(1,\chi)>\frac{C}{(\operatorname{log}D)^c}\]

where c>0 is an absolute constant and C is effectively computable.

 

Event Date: 
March 6, 2014 - 3:30pm to 4:30pm
Location: 
213 MLH
Host: 
Department of Mathematics
Calendar Category: 
Colloquium