Primes In Arithmetic Progressions And Semidefinite Programming

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Primes In Arithmetic Progressions And Semidefinite Programming

Journal Article (2021)

Author(s)

Andrés Chirre (Norwegian University of Science and Technology (NTNU))

Valdir José Pereira Júnior (Instituto Nacional de Matemática Pura e Aplicada - IMPA)

David de Laat (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group

Discrete Mathematics and Optimization

DOI related publication

https://doi.org/10.1090/mcom/3638 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:512b8ef3-65c9-47c6-9533-8d21a09e4dd6

More Info

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Publication Year

2021

Language

English

Research Group

Discrete Mathematics and Optimization

Issue number

331

Volume number

90

Pages (from-to)

2235-2246

Downloads counter

181

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.