Riv. Mat. Univ. Parma, Vol. 12, No. 1, 2021
Kevin Ford ^{[a]}
Large prime gaps and progressions with few primes
Pages: 4147
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 DMS1802139.
Full Text (PDF)
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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