Bounded gaps between primes in Chebotarev sets

Algebra Seminar
Monday, April 28, 2014 - 15:05
1 hour (actually 50 minutes)
Skiles 006
Emory University
A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes $p_1,p_2$ with $|p_1-p_2|\leq 600$ as a consequence of the Bombieri-Vinogradov Theorem.  We apply his general method to the setting of Chebotarev sets of primes.  We study applications of these bounded gaps with an emphasis on ranks of prime quadratic twists of elliptic curves over $\mathbb{Q}$, congruence properties of the Fourier coefficients of normalized Hecke eigenforms, and representations of primes by binary quadratic forms.