acb_dirichlet_platt_multieval, acb_dirichlet_platt_multieval_threaded
#include <flint/acb_dirichlet.h>void acb_dirichlet_platt_multieval(arb_ptr out, const fmpz_t T, slong A, slong B, const arb_t h, const fmpz_t J, slong K, slong sigma, slong prec)sourcevoid acb_dirichlet_platt_multieval_threaded(arb_ptr out, const fmpz_t T, slong A, slong B, const arb_t h, const fmpz_t J, slong K, slong sigma, slong prec)sourceSet out to the values of acb_dirichlet_platt_scaled_lambda on the same grid as acb_dirichlet_platt_scaled_lambda_vec, all at once with discrete Fourier transforms, in the notation of [Pla2017]: is the width of the Gaussian, the number of terms of the Dirichlet series, the number of Taylor terms and sigma an odd integer used in the error bounds. The threaded version uses flint_get_num_threads() threads; the default version decides whether to use threads.
The default version computes the sums over (the bulk of the work) with _dfloat_platt_smk_dd (Sieved power sums and Platt's multi-evaluation) when prec is at most bits, which gives a grid about as accurate as the ball arithmetic version at bits; setting acb_dirichlet_platt_use_dfloat to 0 forces ball arithmetic. In both versions, the part after these sums works at bits (its inputs, of size about 1, carry that accuracy), generates the rows of the gamma factor table for each group of four values of from stored factors and bases instead of storing entries, and sums the convolutions in the frequency domain, in parallel over the groups with one group per thread at a time. The result does not depend on the number of threads.
References#
- [Pla2017] D. J. Platt, "Isolating some non-trivial zeros of zeta", Mathematics of Computation 86 (2017), 2449-2467, https://doi.org/10.1090/mcom/3198
The FLINT team, “acb_dirichlet_platt_multieval, acb_dirichlet_platt_multieval_threaded (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_platt_multieval.html (generated 2026-11-02).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-platt-multieval,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_platt\_multieval, acb\_dirichlet\_platt\_multieval\_threaded (acb\_dirichlet.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_platt_multieval.html},
note = {Generated 2026-11-02}
}