FLINT3.7.0-dev
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acb_theta_sum_radius

Synopsis#include <flint/acb_theta.h>
void acb_theta_sum_radius(arf_t R2, arf_t eps, const arb_mat_t cho, slong ord, slong prec)source

Sets eps to 2−prec2^{-\mathit{prec}} and R2 to a squared radius R2≥max⁡(4,2 ord)R^2 \ge \max(4, 2\,\mathit{ord}) such that (1+8/π)Rg−1+2 orde−R2∏j(1+2π/γj)≤2−prec(1 + \sqrt{8/\pi}) R^{g - 1 + 2\,\mathit{ord}} e^{-R^2} \prod_{j} (1 + \sqrt{2\pi}/\gamma_j) \le 2^{-\mathit{prec}}, where γj\gamma_j are the diagonal entries of CC = cho. For ord = 0, summing over the ellipsoid of radius RR computes θ~a,b\widetilde{\theta}_{a,b} with a tail of absolute value at most eps.

Cite this page

The FLINT team, “acb_theta_sum_radius (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/acb_theta_sum_radius.html (generated 2026-11-02).