FLINT3.7.0-dev
/

_arb_poly_riemann_siegel_theta_series, arb_poly_riemann_siegel_theta_series

Synopsis#include <flint/arb_poly.h>
void _arb_poly_riemann_siegel_theta_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec)source
void arb_poly_riemann_siegel_theta_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec)source

Set res to the Riemann–Siegel theta function

θ(h)=arg⁡Γ ⁣(2ih+14)−log⁡π2h\theta(h) = \arg \Gamma\!\left(\frac{2ih + 1}{4}\right) - \frac{\log \pi}{2} h

of the power series hh, truncated to length n, where the argument of the gamma function is the imaginary part of log⁡Γ\log \Gamma (continuous in hh). The underscore version does not allow aliasing.

Cite this page

The FLINT team, “_arb_poly_riemann_siegel_theta_series, arb_poly_riemann_siegel_theta_series (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_riemann_siegel_theta_series.html (generated 2026-11-02).