acb_modular_epsilon_arg
Synopsis
#include <flint/acb_modular.h>Given g = (a, b; c, d), returns an integer R such that \varepsilon(a,b,c,d) = e^{\pi i R / 12} is the 24th root of unity in the transformation formula of the eta function,
\eta\left(\frac{a\tau+b}{c\tau+d}\right) = \varepsilon(a,b,c,d) \sqrt{c\tau+d} \, \eta(\tau).
Cite this page
The FLINT team, “acb_modular_epsilon_arg (acb_modular.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_modular/acb_modular_epsilon_arg.html (generated 2026-10-20).
@misc{flint-doc-acb-modular-acb-modular-epsilon-arg,
author = {{The FLINT team}},
title = {{acb\_modular\_epsilon\_arg (acb\_modular.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_modular/acb_modular_epsilon_arg.html},
note = {Generated 2026-10-20}
}