5 papers
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…
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…
Rethinking the work of Langlands on Eisenstein series
Devadatta G. Hegde
Chapter of Langlands' monograph "On the functional equations satisfied by Eisenstein series" employs a sophisticated residue scheme to construct a portion of the discrete autom…
Poles of unramified degenerate Eisenstein series
Devadatta G. Hegde
We determine the poles of maximal unramified degenerate Eisenstein series of a split semisimple algebraic group over a number field using a straightforward global argument, avoidin…
Schwartz functions, Hadamard products, and the Dixmier-Malliavin theorem
Devadatta G. Hegde
In this paper we show that functions of the form where and are in…