Primes In Arithmetic Progressions And Semidefinite Programming

Chirre, Andrés; Júnior, Valdir José Pereira; de Laat, D.

Primes In Arithmetic Progressions And Semidefinite Programming

Journal article (2021)

Authors

Andrés Chirre Norwegian University of Science and Technology (NTNU)

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

D. de Laat Discrete Mathematics and Optimization

Research Group

Discrete Mathematics and Optimization

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Published Date

2021

Language

English

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Research Group

Discrete Mathematics and Optimization

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.

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