acb_dirichlet_platt_scaled_lambda
Synopsis
#include <flint/acb_dirichlet.h>Sets res to \Lambda(t) e^{\pi t/4}, where \Lambda(t) = \pi^{-it/2} \Gamma(\frac{1/2+it}{2}) \zeta(\frac12 + it) is defined at the beginning of §3 of [Pla2017]. By the functional equation it is real for real t, it has the same zeros as \zeta(1/2 + it) [Pla2011], and the exponential factor cancels the decay of the gamma factor.
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
- [Pla2011] D. J. Platt, "Computing degree 1 L-functions rigorously", Ph.D. Thesis, University of Bristol (2011), https://people.maths.bris.ac.uk/~madjp/thesis5.pdf
Cite this page
The FLINT team, “acb_dirichlet_platt_scaled_lambda (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_scaled_lambda.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-platt-scaled-lambda,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_platt\_scaled\_lambda (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_scaled_lambda.html},
note = {Generated 2026-10-20}
}