FLINT3.7.0-dev
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acb_modular_theta_const_sum, acb_modular_theta_const_sum_basecase, acb_modular_theta_const_sum_rs

Synopsis#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)source
void acb_modular_theta_const_sum_basecase(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec)source
void acb_modular_theta_const_sum_rs(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec)source

Compute the theta constants θ2(0,τ)/q1/4\theta_2(0, \tau)/q_{1/4}, θ3(0,τ)\theta_3(0, \tau) and θ4(0,τ)\theta_4(0, \tau) from q=eπiτq = e^{\pi i \tau} without a modular transformation. The basecase and rs versions sum the truncated series ∑qk(k+1)\sum q^{k(k+1)}, ∑qk2\sum q^{k^2} and ∑(−1)kqk2\sum (-1)^k q^{k^2} over the k∈Zk \in \mathbb{Z} with exponent less than NN, with a short addition sequence and with rectangular splitting respectively [EHJ2016], without a tail bound. acb_modular_theta_const_sum chooses NN from ∣q∣|q| and prec, uses the basecase for N<1800N < 1800 and adds the truncation error.

References#

Cite this page

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 2026-11-02).