Simple zeros of $\mathrm{GL}(2)$ $L$-functions

Alexandre de Faveri

Let $f\in S_k(\hat{I}{“}_1(N))$ be a primitive holomorphic form of arbitrary weight $k$ and level $N$. We show that the completed $L$-function of $f$ has $\hat{I}\text{c◯}\left(T^{\hat{I}}´\right)$ simple zero…