Riv. Mat. Univ. Parma, Vol. 12, No. 1, 2021

Kevin Ford [a]

Large prime gaps and progressions with few primes

Pages: 41-47
Received: August 3, 2019
Accepted in revised form: February 19, 2020
Mathematics Subject Classification (2010): Primary: 11N05, 11N13; Secondary 11M20.
Keywords: Primes, prime gaps, primes in progressions, exceptional zero, exceptional character.
Author address:
[a]: Department of Mathematics, University of Illinois, 1409 West Green St, Urbana, IL 61801, USA.

The author was supported by National Science Foundation grant DMS-1802139.

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Abstract: We show that the existence of arithmetic progressions with few primes, with a quantitative bound on ''few'', implies the existence of larger gaps between primes less than \(x\) than is currently known unconditionally. In particular, we derive this conclusion if there are certain types of exceptional zeros of Dirichlet \(L\)-functions.

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