Primes In Arithmetic Progressions And Semidefinite Programming

Andrés Chirre*, Valdir José Pereira Júnior, David de Laat

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed by Carneiro, Milinovich and Soundararajan [Comment. Math. Helv. 94, no. 3 (2019)]. For this we extend the Guinand-Weil explicit formula over all Dirichlet characters modulo q ≥ 3, and we reduce the associated extremal problems to convex optimization problems that can be solved numerically via semidefinite programming.

Original languageEnglish
Pages (from-to)2235-2246
Number of pages12
JournalMathematics of Computation
Volume90
Issue number331
DOIs
Publication statusPublished - 2021

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