FLINT3.7.0-dev
/

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 β(t)=1/6+log⁡log⁡t/log⁡t\beta(t) = 1/6 + \log\log t / \log t, the exponent in the bound ∣ζ(1/2+it)∣=O(tβ(t))|\zeta(1/2 + it)| = O(t^{\beta(t)}) used in [Pla2017].

References#

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 2026-11-02).