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