On the absolute convergence of automorphic Dirichlet series

2021/05/14 by Raghunathan, Ravi
#11F66 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2105.06957

Abstract

Let F(s)=∑_n=1^∞(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 ∑_n

Related

• Beyond the extended Selberg class: 1
• Beyond the extended Selberg class: d_F≤ 1
• Dirichlet series constructed from periods of automorphic forms
• Oscillations of coefficients of Dirichlet series attached to automorphic forms
• Dirichlet series associated to sum-of-digits functions