acb_dirichlet_backlund_s
Synopsis
#include <flint/acb_dirichlet.h>Sets res to S(t) = \frac{1}{\pi}\operatorname{arg}\zeta(\frac{1}{2} + it), where the argument is defined by continuous variation from s = 2 to 2 + it and then to \frac12 + it, not the principal value. It is computed as N(t) - \theta(t)/\pi - 1.
Cite this page
The FLINT team, “acb_dirichlet_backlund_s (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_backlund_s.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-backlund-s,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_backlund\_s (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_backlund_s.html},
note = {Generated 2026-10-20}
}