PreprintCC BY 4.0arXiv
Simple and accurate approximations to Dirichlet L-functions
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.
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BibTeX
@misc{kuznetsov2026simple,
title = {{Simple and accurate approximations to Dirichlet $L$-functions}},
author = {Alexey Kuznetsov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10595},
eprint = {2610.10595},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10595},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simple and accurate approximations to Dirichlet L-functions
AU - Alexey Kuznetsov
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.10595
UR - https://arxiv.org/abs/2610.10595
AB - 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.
ER -