Computing Dirichlet character sums to a power-full modulus

2012/05/21 by Ghaith A. Hiary, Hiary, Ghaith A. · 1 citation
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1205.4687

openalex publication_date 2012/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Postnikov character formula is used to express large portions of a Dirichlet character sum in terms of quadratic exponential sums. The quadratic sums are then computed using an analytic algorithm previously derived by the author. This leads to a power-saving if the modulus is smooth enough. As an application, a fast, and potentially practical, method to compute Dirichlet L-functions with complexity exponent 1/3 for smooth enough moduli is derived.

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