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Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups
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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BibTeX
@misc{hou2026fourier,
title = {{Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups}},
author = {Alan Xuelun Hou and Yusheng Lei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.24719},
eprint = {2608.24719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24719},
}
RIS
TY - UNPB
TI - Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups
AU - Alan Xuelun Hou
AU - Yusheng Lei
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2608.24719
UR - https://arxiv.org/abs/2608.24719
AB - 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.
ER -