: Mathématiques: Riemann-Siegel theta function

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Riemann-Siegel theta function

In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as
${\\displaystyle \ heta (t)=\\arg \\left(\\Gamma \\left({\ rac {1}{4}}+{\ rac {it}{2}}\ ight)\ ight)-{\ rac {\\log \\pi }{2}}t}$
for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and ${\\displaystyle \ heta (0)=0}$ holds, i.e., in the same way that the principal branch of the log-gamma function is defined.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_theta_function)

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