acb_mzeta_epstein_crandall
Synopsis
#include <flint/acb_mzeta.h>int acb_mzeta_epstein_crandall(acb_t res, const acb_t nu, const arb_mat_t A, arb_srcptr x, arb_srcptr y, int flags, acb_mzeta_cache_t cache, slong prec)sourceEvaluates Crandall's representation [BBG2024, Thm. 2.11], which writes as two exponentially convergent sums of incomplete gamma functions over and , term by term in ball arithmetic, for any , and precision. The sums are truncated rigorously with the tail bound of theta series; their number of terms grows like for bits. With an exact Gram matrix, the incomplete gamma function is evaluated once per value of the quadratic form. See Crandall's representation and Term-by-term summation.
References#
- [BBG2024] A. A. Buchheit, J. K. Busse and R. Gutendorf, "Computation and properties of the Epstein zeta function with high-performance implementation in EpsteinLib", preprint (2024), https://arxiv.org/abs/2412.16317
Cite this page
The FLINT team, “acb_mzeta_epstein_crandall (acb_mzeta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_mzeta/acb_mzeta_epstein_crandall.html (generated 2026-11-07).
@misc{flint-doc-acb-mzeta-acb-mzeta-epstein-crandall,
author = {{The FLINT team}},
title = {{acb\_mzeta\_epstein\_crandall (acb\_mzeta.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_mzeta/acb_mzeta_epstein_crandall.html},
note = {Generated 2026-11-07}
}