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