D. G. Hegde

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20212026

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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.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…