Computing Dirichlet character sums to a power-full modulus

JOURNAL OF NUMBER THEORY

卷:140

Article

Hiary, Ghaith A.

关键词: Character sums;    Exponential sums;    Dirichlet L-functions;    Algorithms;   

DOI  :  10.1016/j.jnt.2013.12.005

来源: Elsevier

【 摘 要 】

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. Published by Elsevier Inc.

【 授权许可】

Free