Year: 2026
Type: preprint
Abstract: We study degenerate Eisenstein series on symplectic groups and construct a new automorphic descent. We show that a certain Fourier coefficient, after restriction to a smaller symplectic group, is itself an Eisenstein series with the same inducing parameter \(s\). We describe the resulting holomorphic section explicitly in terms of the original section and local \(L\)-factors at unramified places. At every regular point of the local descent, we prove surjectivity at non-Archimedean places and dense image at Archimedean places. We finally indicate an application of the iterated descent to maximal Fourier coefficients of Eisenstein series.
Source: arXiv (Cornell University)
Authors: Hou, Alan Xuelun, Lei, Yusheng
Institution: Brandeis University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204234114