Bounded Gaps Between Primes in Chebotarev Sets

Abstract

A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes $p_1,p_2$ with $|p_1-p_2|\le 600$ as a consequence of the Bombieri-Vinogradov Theorem. In this paper, 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.

15 pages. Referee comments implemented. Research in the Mathematical Sciences 2014, 1:4

References in corpus (1)

• Primes in intervals of bounded length

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