Computing Dirichlet character sums to a power-full modulus

Ghaith A. Hiary

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arXiv · 1205.4687

Computing Dirichlet character sums to a power-full modulus

Ghaith A. Hiary

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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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Ghaith A. Hiary. 2012-05-21. Computing Dirichlet character sums to a power-full modulus. https://arxiv.org/abs/1205.4687

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