Fourier optimization and the least quadratic non-residue
Speaker: Emily Quesada-Herrera
Date: Mon, Jan 29, 2024
Location: PIMS, University of Lethbridge, Online, Zoom
Conference: Analytic Aspects of L-functions and Applications to Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Mon, Jan 29, 2024
Location: PIMS, University of Lethbridge, Online, Zoom
Conference: Analytic Aspects of L-functions and Applications to Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
We will explore how a Fourier optimization framework may be used to study two classical problems in number theory involving Dirichlet characters: The problem of estimating the least character non-residue; and the problem of estimating the least prime in an arithmetic progression. In particular, we show how this Fourier framework leads to subtle, but conceptually interesting, improvements on the best current asymptotic bounds under the Generalized Riemann Hypothesis, given by Lamzouri, Li, and Soundararajan. Based on joint work with Emanuel Carneiro, Micah Milinovich, and Antonio Ramos.
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