Additive twist of a cusp-form L-function
= Additive twist of a cusp-form L-function
{title2=$L(f,a/N,s)=\sum_{n\geq1}c_ne^{2\pi ian/N}n^{-s}$}
For a <cusp form> $f=\sum c_nq^n$ and coprime integers $a,N$, the additive twist inserts the additive character $e^{2\pi ian/N}$. It is the <Dirichlet series> associated with the rational translate $f(a/N+\tau)$. Its completed <Mellin transform> uses the scale $N^s$ and the <Gamma function>.