`acb_dirichlet_backlund_s`

Synopsis#include <flint/acb_dirichlet.h>

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

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 2026-11-02).

@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 2026-11-02}
}

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