acb_dirichlet_platt_lemma_32, acb_dirichlet_platt_lemma_A5, acb_dirichlet_platt_lemma_A7, acb_dirichlet_platt_lemma_A9, acb_dirichlet_platt_lemma_A11, acb_dirichlet_platt_lemma_B1, acb_dirichlet_platt_lemma_B2
#include <flint/acb_dirichlet.h>void acb_dirichlet_platt_lemma_32(arb_t out, const arb_t h, const arb_t t0, const arb_t x, slong prec)sourcevoid acb_dirichlet_platt_lemma_A7(arb_t out, slong sigma, const arb_t t0, const arb_t h, slong k, slong A, slong prec)sourcevoid acb_dirichlet_platt_lemma_A9(arb_t out, slong sigma, const arb_t t0, const arb_t h, slong A, slong prec)sourcevoid acb_dirichlet_platt_lemma_A11(arb_t out, const arb_t t0, const arb_t h, slong B, slong prec)sourcevoid acb_dirichlet_platt_lemma_B1(arb_t out, slong sigma, const arb_t t0, const arb_t h, const fmpz_t J, slong prec)sourcevoid acb_dirichlet_platt_lemma_B2(arb_t out, slong K, const arb_t h, const arb_t xi, slong prec)sourceSet out to the error bounds of Lemma 3.2 and Lemmas A.5, A.7, A.9, A.11, B.1 and B.2 of [Pla2017], which bound the errors of the grid evaluation in acb_dirichlet_platt_multieval (truncation of the Dirichlet series, of the Taylor expansion, aliasing of the discrete Fourier transform, and so on). Lemma A.5 requires B > h\sqrt{k}; when a lemma's hypotheses fail, the bound is infinite.
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_lemma_32, acb_dirichlet_platt_lemma_A5, acb_dirichlet_platt_lemma_A7, acb_dirichlet_platt_lemma_A9, acb_dirichlet_platt_lemma_A11, acb_dirichlet_platt_lemma_B1, acb_dirichlet_platt_lemma_B2 (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_lemma_32.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-platt-lemma-32,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_platt\_lemma\_32, acb\_dirichlet\_platt\_lemma\_A5, acb\_dirichlet\_platt\_lemma\_A7, acb\_dirichlet\_platt\_lemma\_A9, acb\_dirichlet\_platt\_lemma\_A11, acb\_dirichlet\_platt\_lemma\_B1, acb\_dirichlet\_platt\_lemma\_B2 (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_lemma_32.html},
note = {Generated 2026-10-20}
}