acb_elliptic_zeta
Synopsis
#include <flint/acb_elliptic.h>Sets res to the Weierstrass zeta function \zeta(z, \tau) = z^{-1} + \sum_{\omega \ne 0} ((z - \omega)^{-1} + \omega^{-1} + z \omega^{-2}), which satisfies \zeta' = -\wp and is quasi-periodic: \zeta(z + 1) = \zeta(z) + 2\eta_1, \zeta(z + \tau) = \zeta(z) + 2\eta_3 with \eta_1 = \zeta(1/2) and \eta_3 = \zeta(\tau/2). It is computed as \zeta(z) = 2 \eta_1 z + \theta_1'(z, \tau)/\theta_1(z, \tau), where \eta_1 = -\theta_1'''(0, \tau) / (6 \theta_1'(0, \tau)).
Cite this page
The FLINT team, “acb_elliptic_zeta (acb_elliptic.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_elliptic/acb_elliptic_zeta.html (generated 2026-10-20).
@misc{flint-doc-acb-elliptic-acb-elliptic-zeta,
author = {{The FLINT team}},
title = {{acb\_elliptic\_zeta (acb\_elliptic.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_elliptic/acb_elliptic_zeta.html},
note = {Generated 2026-10-20}
}