On the absolute convergence of automorphic Dirichlet series
- Resource Type
- Working Paper
- Authors
- Raghunathan, Ravi
- Source
- Subject
- Mathematics - Number Theory
11F66, 11M41
- Language
Let $F(s)=\sum_{n=1}^{\infty}\frac{a_n}{n^s}$ be a Dirichlet series in the axiomatically defined class ${\mathfrak A}^{\#}$ . The class ${\mathfrak A}^{\#}$ is known to contain the extended Selberg class ${\mathcal S}^{\#}$, as well as all the $L$-functions of automorphic forms on $GL_n/K$, where $K$ is a number field. Let $d$ be the degree of $F(s)$. We show that $\sum_{nComment: 9 pages