acb_modular_eta_sum
Synopsis
#include <flint/acb_modular.h>Sets eta to \prod_{n \ge 1} (1 - q^n) = \sum_{k \in \mathbb{Z}} (-1)^k q^{k(3k-1)/2}, the eta function without the factor e^{\pi i \tau / 12}, given q = e^{2\pi i \tau}, by summing the pentagonal number series with a rigorous tail bound. Like acb_modular_theta_sum, it is meant for |q| \ll 1. The series is summed with a short addition sequence, or with rectangular splitting from 400 terms [EHJ2016].
References#
- [EHJ2016] A. Enge, W. Hart and F. Johansson, "Short addition sequences for theta functions", preprint (2016), https://arxiv.org/abs/1608.06810
Cite this page
The FLINT team, “acb_modular_eta_sum (acb_modular.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_modular/acb_modular_eta_sum.html (generated 2026-10-20).
@misc{flint-doc-acb-modular-acb-modular-eta-sum,
author = {{The FLINT team}},
title = {{acb\_modular\_eta\_sum (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_eta_sum.html},
note = {Generated 2026-10-20}
}