This analysis improves asymptotic bounds in number theory for least quadratic non-residue and least prime in arithmetic progression, suggesting deeper links to Dirichlet L-functions.
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.
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Carneiro et al. (2025) studied this question.
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