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arXiv · 2608.24719

Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups

Alan Xuelun Hou·Yusheng Lei
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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.

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Alan Xuelun Hou, Yusheng Lei. 2026-08-25. Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups. https://arxiv.org/abs/2608.24719

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