A mean square formula for central values of twisted automorphic L-functions

A Trace Formula of Special Values of Automorphic L-functions

Deligne introduced the concept of special values of automorphic L-functions. The arithmetic properties of these L-functions play a fundamental role in modern number theory. In this paper we prove a trace formula which relates special values of the Hecke, Rankin, and the central value of the Garrett triple L-function attached to primitive newforms. This type of trace formula is new and involves ...

The Cubic Moment of Central Values of Automorphic L-functions

Twisted Moments of Automorphic L-functions

We study the moments of the symmetric power L-functions of primitive forms at the edge of the critical strip twisted by the square of the value of the standard L-function at the center of the critical strip. We give a precise expansion of the moments as the order goes to infinity. CONTENTS

Sums of Twisted Gl ( 3 ) Automorphic L - Functions

Let F be a number field and π be an automorphic representation on GLr (AF ). In this paper we consider weighted sums of quadratic twists of the L-function for π , ∑ d L(s, π, χd ) a(s, π, d) Nd −w , where χd is a quadratic character roughly attached to F( √ d)/F . We analyze the properties which the weights a(s, π, d) must satisfy if this is to satisfy a (certain, non-abelian) group of function...

Liftings and Mean Value Theorems for Automorphic L-functions