Year: 2026
Type: preprint
Abstract: We extend the quadrature method developed in [10] to Dirichlet $L$-functions associated with primitive characters. The approximations combine finite Dirichlet sums with correction terms whose quadrature coefficients can be precomputed for each character. Numerical experiments demonstrate high accuracy in the critical strip and in other vertical strips. We also describe how to combine these approximations with direct summation and Euler--Maclaurin summation to evaluate $L(s,χ)$ throughout the complex plane.
Source: arXiv (Cornell University)
Author: Kuznetsov, Alexey
Institution: York University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221106148