Oscillations of coefficients of Dirichlet series attached to automorphic forms
Oscillations of coefficients of Dirichlet series attached to automorphic forms
For $m\ge 2$, let $\pi$ be an irreducible cuspidal automorphic representation of $GL_m(\mathbb {A}_{\mathbb {Q}})$ with unitary central character. Let $a_\pi (n)$ be the $n^{th}$ coefficient of the $L$-function attached to $\pi$. Goldfeld and Sengupta have recently obtained a bound for $\sum _{n\le x} a_\pi (n)$ as $x \rightarrow \infty$. …