`acb_dirichlet_platt_beta`

Synopsis#include <flint/acb_dirichlet.h>

void acb_dirichlet_platt_beta(arb_t res, const arb_t t, slong prec)source

Sets res to \beta(t) = 1/6 + \log\log t / \log t, the exponent in the bound |\zeta(1/2 + it)| = O(t^{\beta(t)}) used in [Pla2017].

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

Cite this page

The FLINT team, “acb_dirichlet_platt_beta (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_beta.html (generated 2026-10-20).

@misc{flint-doc-acb-dirichlet-acb-dirichlet-platt-beta,
  author       = {{The FLINT team}},
  title        = {{acb\_dirichlet\_platt\_beta (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_beta.html},
  note         = {Generated 2026-10-20}
}

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