Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression
Year: 2025
Type: article
Abstract: By means of a Fourier optimization framework, we improve the current asymptotic bounds under the Generalized Riemann Hypothesis for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of estimating the least prime in an arithmetic progression. In an appendix, we illustrate the connection between bounds for the argument of Dirichlet L L -functions on the critical line and bounds for the least quadratic non-residue.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4154
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Zeros of L-functions and Arithmetic, G1941594282, G2569510917, G2742791625, G2993639851, G327966385, G3464052157, G3896130171, G3960284857, Local statistics of arithmetic sequences, G6712437350, G7250818260, G7431982298, G7807862245, G7849852887, The Distribution of Zeros of L-Functions and Related Questions, G8205490244, Randomness and Determinism in Analysis and Number Theory, G896413585, G898156678
OpenAlex ID: W4416925497