I'm looking for a functional equation for the following Dirichlet series
$$\varphi(s)=\sum_{n=1}^{+\infty}{\frac{2 \cos(2n \pi q)}{n^s}}$$
where $q$ is a rational number.
Any help ?
2026-03-25 11:12:38.1774437158
A functional equation for a Dirichlet series
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