Family of Approximations for Dirichlet L-functions

2023/11/30 by Alzergani, Mohammed
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.18816

Abstract

We introduce an infinite family of approximations for a Dirichlet L-function L(s, χ) arising from truncated Euler products. These approximations are entire functions and satisfy the same functional equation as L(s, χ). We provide numerical evidence of the accuracy of estimating values of L(s, χ) in the critical strip using these approximations. We then provide a precise expression for the error of the approximations and show that the error has exponential decay in largest prime considered in the truncated Euler product.

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