3 papers
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…
math.NT2024
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…