A Note on Spectral Analysis in Automorphic Representation Theory for ${\rm GL}_2$: II

TL;DR

This paper extends Zagier's regularized integral techniques to singular cases within automorphic representation theory for GL_2, providing tools crucial for progress on subconvexity problems.

Contribution

It introduces generalized methods for regularized integrals in singular scenarios, enhancing the analytical toolkit for automorphic forms and subconvexity research.

Findings

Developed generalized regularized integral techniques for singular cases.

Applied methods to the context of triple product formulas.

Facilitated progress on subconvexity problems for GL_2.

Abstract

We generalize Zagiers work on regularized integral to the singular case in the adelic setting. We develop necessary tools of treating various singular cases of regularized triple product formulas, which appear naturally in the work of Michel and Venkatsh on the subconvexity problem for $GL_2$.