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

2024/04/12 by Emanuel Carneiro, Carneiro, Emanuel, Micah B. Milinovich +5
Computer Science · Mathematics · #11M06 #11M26 #11N13 #42A38 #65K05 #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.2404.08380

openalex publication_date 2024/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Fourier optimization and consequences of the generalized Riemann hypothesis
• Fourier optimization and quadratic forms
• Conditional bounds for the least quadratic non-residue and related\n problems
• Primes in arithmetic progressions and semidefinite programming
• Discrete Fourier Transform and L-functions