# MathCS Seminar

Title: An Effective Log-Free Zero Density Estimate for Automorphic $L$-functions and the Sato-Tate Conjecture
Seminar: Algebra
Speaker: Jesse Thorner of Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-31 at 4:00PM
Venue: W304
Abstract:
The classical techniques used to put primes in intervals of the form $[x,2x]$ are insufficient to put primes in intervals of the form $[x,x+x^{1-\delta}]$ for any $\delta>0$, or to find the least prime in an arithmetic progression $a\bmod q$. Such problems are easily answered assuming the Generalized Riemann Hypothesis, but they can be answered unconditionally using very detailed information about the location and density of zeros of Dirichlet $L$-functions in regions of the critical strip. We will discuss effective results on the distribution of general automorphic $L$-functions in the critical strip and use these distribution results to study generalizations of the aforementioned problems in the context of the Sato-Tate Conjecture.