Evaluating $L$-functions with few known coefficients
Number Theory
2019-02-20 v2
Abstract
We address the problem of evaluating an -function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that is possible to evaluate the -function more precisely than one would expect from the standard approach. The method, however, requires considerably more computational effort to achieve a given accuracy than would be needed if more Dirichlet coefficients were available.
Cite
@article{arxiv.1211.4181,
title = {Evaluating $L$-functions with few known coefficients},
author = {David W. Farmer and Nathan C. Ryan},
journal= {arXiv preprint arXiv:1211.4181},
year = {2019}
}
Comments
14 pages; Added a new section where we evaluate L(1/2 + 100 i, Delta) to 42 decimal places using no Dirichlet series coefficients at all