Automorphic Forms, Definite Quaternion Algebras, and Atkin–Lehner Theory on Trees

Families of automorphic forms on definite quaternion algebras and Teitelbaum’s conjecture

Trees, Quaternion Algebras and Modular Curves

We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over Fq(T ) and discuss applications to arithmetic geometry and group theory.

Modern Theory of Automorphic Forms ∗

The modern theory of automorphic forms is a response to many different impulses and influences, above all the work of Hecke, but also class-field theory and the study of quadratic forms, the theory of representations of reductive groups, and of complexmultiplication, but so far many of the most powerful techniques are the issue, direct or indirect, of the introduction by Maass and then Selberg ...

Explicit Calculations of Automorphic Forms for Definite Unitary Groups

I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(Ẑ) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic f...

String duality, automorphic forms, and generalized Kac-Moody algebras

finding the pole requires analytic continuation unless there are boundstates at threshhold in the sector Q1 + Q2. The residue of the pole must be expressed in terms of matrix elements with on-shell states. By charge conservation and the Bogomolnyi bound these states must be the BPS states in the superselection sectorQ1+Q2. Therefore the residue of the pole “factors through” the space of BPS sta...