Riemann–Siegel theta function

In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as θ ( t ) = arg ⁡ ( Γ ( 1 4 + i t 2 ) ) − log ⁡ π 2 t {\displaystyle \theta (t)=\arg \left(\Gamma \left({\frac {1}{4}}+{\frac {it}{2}}\right)\right)-{\frac {\log \pi }{2}}t} for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and θ ( 0 ) = 0 {\displaystyle \theta (0)=0} holds, i.e., in the same way that the principal branch of the log-gamma function is defined.

Source: Wikipedia — Riemann–Siegel theta function (CC BY-SA 4.0)