Estimates for character sums and Dirichlet L-functions to smooth moduli

2015/03/24 by A. J. Irving, Irving, A. J. · 1 citation
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1503.07156

openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the q-analogue of van der Corput's method to estimate short character sums to smooth moduli. If χ is a primitive Dirichlet character modulo a squarefree, q^δ-smooth integer q we show that L(\frac12,χ)≪_εq^{(27)/(164)+O(δ)+ε}.

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• Primes in simultaneous arithmetic progressions

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• Computing Dirichlet character sums to a power-full modulus
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