  Given a degree 1 function $F\in\mathcal{S}^{\sharp}$ and a real number
$\alpha$, we consider the linear twist $F(s,\alpha)$, proving that it satisfies
a functional equation reflecting $s$ into $1-s$, which can be seen as a
Hurwitz-Lerch type of functional equation. We also derive some results on the
distribution of the zeros of the linear twist.
