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.
Original language | English (US) |
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Pages (from-to) | 41-47 |
Number of pages | 7 |
Journal | Rivista di Matematica della Universita di Parma |
Volume | 12 |
Issue number | 1 |
State | Published - 2021 |
Keywords
- Primes
- exceptional character
- exceptional zero
- prime gaps
- primes in progressions
ASJC Scopus subject areas
- General Mathematics