The prime number theorem for automorphic L-functions for

✍ Scribed by Yan Qu

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 159 KB
• Volume: 122
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.03.007

✦ Synopsis

Let π be irreducible unitary cuspidal representation of GL m (A Q ) with m 2, and L(s, π ) the L-function attached to π . The prime counting function ψ(x, π) is studied under the Generalized Riemann Hypothesis for L(s, π ). It is proved that ψ(x, π) x 1/2 (log log x) 2 , except on a set of x of finite logarithmic measure. Furthermore, the integral mean square of ψ(x, π) is evaluated.