A Prime Number Theorem for Rankin-Selberg L-functions over Number fields

2009/10/19 by Gillespie, Tim, Ji, Guanghua
#11M99 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0910.3660

Abstract

We prove a prime number theorem first for the classical Rankin-Selberg L-function L(s,π×π') over any Galois extension with π and π' unitary automorphic cuspidal representations of GL_n and GL_m respectively with at least one of the representations subject to a self-contragredient assumption. We then extend these results to two representations π defined on GL_n/E and π' defined on GL_m/F with E and F cylic algebraic number fields of coprime degree where π and π' admit a base change lift from ℚ again given a self-contragredient assumption on at least one of the representations which lift to π or π'.

Related

• Solvable Base Change and Rankin-Selberg Convolutions
• Rankin-Selberg L-functions in cyclotomic towers, III
• Tatuzawa's theorem for Rankin-Selberg L-functions
• Lower Bounds for Rankin-Selberg L-functions on the Edge of the Critical Strip
• Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field