College of Liberal Arts & Sciences
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