TWISTS OF AUTOMORPHIC L-FUNCTIONS AT THE CENTRAL POINT

Cubic Twists of Gl(2) Automorphic L-functions

Let K = Q(√−3) and let π be a cuspidal automorphic representation of GL(2, AK). Consider the family of twisted L-functions L(s, π⊗χ) where χ ranges over the cubic Hecke characters of K. In this paper the mean value of this family of L-functions is computed; the result is consistent with the generalized Lindelöf hypothesis. From this mean value result a nonvanishing theorem is established: for g...

The Cubic Moment of Central Values of Automorphic L-functions

Non-vanishing of Dirichlet L-functions at the Central Point

Lectures on automorphic L-functions

PREFACE This article follows the format of five lectures that we gave on automorphic Lfunctions. The lectures were intended to be a brief introduction for number theorists to some of the main ideas in the subject. Three of the lectures concerned the general properties of automorphic L-functions, with particular reference to questions of spectral decomposition. We have grouped these together as ...

Nonvanishing of Gl ( 2 ) automorphic L functions at 1 / 2

Let k be a number field with ring of adeles A, let B be a quaternion algebra defined over k, and letG = B×. Let π be an infinite dimensional irreducible cuspidal automorphic representation of G(A). Then the vanishing or nonvanishing of L(1/2, π) has been conjectured or shown to be equivalent to conditions of considerable interest in number theory or automorphic representation theory. For exampl...