`acb_dirichlet_platt_scaled_lambda`

Synopsis#include <flint/acb_dirichlet.h>

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

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 2026-11-02).

@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 2026-11-02}
}

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