FLINT3.7.0-dev
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acb_mzeta_epstein_theta

Synopsis#include <flint/acb_mzeta.h>
int acb_mzeta_epstein_theta(acb_t res, const acb_t nu, const arb_mat_t A, arb_srcptr x, arb_srcptr y, int flags, acb_mzeta_cache_t cache, slong prec)source

Writes each of the two Crandall sums as a Mellin integral ∫1∞wa−1Θ(w) dw\int_1^\infty w^{a-1} \Theta(w)\, dw of a Riemann theta function and computes it by Gauss–Legendre quadrature with rigorous error bounds, using acb_theta_one for small ww and direct sums over a few lattice points for large ww; see Mellin integrals of theta functions. The cost is about PP integrand values per sum at PP bits instead of O(Pd/2)O(P^{d/2}) terms, so this method is preferable to acb_mzeta_epstein_crandall at high precision. Applies for d≤8d \le 8. The computation is parallel with up to flint_get_num_threads() threads, and the result does not depend on the number of threads.

Cite this page

The FLINT team, “acb_mzeta_epstein_theta (acb_mzeta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_mzeta/acb_mzeta_epstein_theta.html (generated 2026-11-07).