The generalized prime number theorem for automorphic L-functions

Abstract

Let π and π′ be automorphic irreducible cuspidal representations of GL _m(ℚ$\mathbb{Q}_\mathbb{A} $) and GL _m′ (ℚ$\mathbb{Q}_\mathbb{A} $), respectively, and L(s, π × $\tilde \pi '$) be the Rankin-Selberg L-function attached to π and π′. Without assuming the Generalized Ramanujan Conjecture (GRC), the author gives the generalized prime number theorem for L(s, π × $\tilde \pi '$) when π ≅ π′. The result generalizes the corresponding result of Liu and Ye in 2007.

Keywords

Perron’s formula / Prime number theorem / Rankin-Selberg L-functions

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