Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression

Antonio Pedro Ramos; Emanuel Carneiro; Emily Quesada-Herrera; Micah B. Milinovich

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arxiv 2404.08380 v2 pith:US25KBI4 submitted 2024-04-12 math.NT math.CA

Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression

Emanuel Carneiro , Micah B. Milinovich , Emily Quesada-Herrera , Antonio Pedro Ramos This is my paper

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keywords leastprimearithmeticestimatingfouriernon-residueoptimizationproblem

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By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH 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.

Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression

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