acb_modular_theta_const_sum, acb_modular_theta_const_sum_basecase, acb_modular_theta_const_sum_rs
#include <flint/acb_modular.h>void acb_modular_theta_const_sum(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong prec)sourcevoid acb_modular_theta_const_sum_basecase(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec)sourcevoid acb_modular_theta_const_sum_rs(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec)sourceCompute the theta constants \theta_2(0, \tau)/q_{1/4}, \theta_3(0, \tau) and \theta_4(0, \tau) from q = e^{\pi i \tau} without a modular transformation. The basecase and rs versions sum the truncated series \sum q^{k(k+1)}, \sum q^{k^2} and \sum (-1)^k q^{k^2} over the k \in \mathbb{Z} with exponent less than N, with a short addition sequence and with rectangular splitting respectively [EHJ2016], without a tail bound. acb_modular_theta_const_sum chooses N from |q| and prec, uses the basecase for N < 1800 and adds the truncation error.
References#
- [EHJ2016] A. Enge, W. Hart and F. Johansson, "Short addition sequences for theta functions", preprint (2016), https://arxiv.org/abs/1608.06810
The FLINT team, “acb_modular_theta_const_sum, acb_modular_theta_const_sum_basecase, acb_modular_theta_const_sum_rs (acb_modular.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_modular/acb_modular_theta_const_sum.html (generated 2026-10-20).
@misc{flint-doc-acb-modular-acb-modular-theta-const-sum,
author = {{The FLINT team}},
title = {{acb\_modular\_theta\_const\_sum, acb\_modular\_theta\_const\_sum\_basecase, acb\_modular\_theta\_const\_sum\_rs (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_theta_const_sum.html},
note = {Generated 2026-10-20}
}