Pairings of automorphic distributions

The Rankin-Selberg method for automorphic distributions

We recently established the holomorphic continuation and functional equation of the exterior square L-function for GL(n,Z), and more generally, the archimedean theory of the GL(n) exterior square L-function over Q. We refer the reader to our paper [15] for a precise statement of the results and their relation to previous work on the subject. The purpose of this note is to give an account of our...

The Highly Oscillatory Behavior of Automorphic Distributions for SL(2)

Automorphic distributions for SL(2) arise as boundary values of modular forms and, in a more subtle manner, from Maass forms. In the case of modular forms of weight one or of Maass forms, the automorphic distributions have continuous first antiderivatives. We recall earlier results of one of us on the Hölder continuity of these continuous functions and relate them to results of other authors; t...

Tangent Lines to Curves Arising from Automorphic Distributions

Automorphic distributions arise in connection with boundary values of modular forms and Maass forms. In most cases, these distributions have antiderivatives that are continuous functions. We shall look at the result of graphing the real vs. imaginary parts of these functions. Because of the automorphic properties of the distributions we consider, the graphs of their antiderivatives are curves w...

Automorphic distributions , L - functions , and Voronoi summation for GL

for the error term in Gauss’ classical circle problem, improving greatly on Gauss’ own bound O(x1/2). Though Voronoi originally deduced his formulas from Poisson summation in R2, applied to appropriately chosen test functions, one nowadays views his formulas as identities involving the Fourier coefficients of modular forms on GL(2), i.e., modular forms on the complex upper half plane. A discuss...

Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)