D. G. Hegde

collaborators

4 papers

math.RT2026

A simple construction of the automorphic residual spectrum

Devadatta G. Hegde

We consider the spherical Borel Eisenstein series induced from the trivial representation for a split semisimple linear algebraic group over a number field. We prove that its regul…

math.NT2026

On Franke's theorem in the simplest case

Devadatta G. Hegde

For level one spherical automorphic forms on the upper half-plane, we prove directly that every automorphic form is a sum of a cusp form and a linear combination of Laurent coeffic…

math.NT2026

Rethinking the work of Langlands on Eisenstein series

Devadatta G. Hegde

Chapter $7$ of Langlands' monograph "On the functional equations satisfied by Eisenstein series" employs a sophisticated residue scheme to construct a portion of the discrete autom…

math.RT2021

Schwartz functions, Hadamard products, and the Dixmier-Malliavin theorem

Devadatta G. Hegde

In this paper we show that functions of the form $\prod_{n \geq 1} \frac{1}{( 1 + \frac{x ^{2}}{a _{n}^{2}} )}$ where $a_{n} > 0$ and $\sum_{n \geq 1} \frac{1}{a _{n}^{2}} < \infty$ are in…