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Fourier Coefficients of Siegel-Eisenstein Series of Degree 2m and Weight m+1
Abstract
We study Fourier coefficients of the Siegel-Eisenstein series Em+1(2m)(Z) for m≡1pmod4 and m≥5. Using the Fourier expansion formula due to Mizumoto, we determine the constant term and the exceptional non-zero Fourier coefficients. The result gives a higher-degree analogue of the degree-two formulas of Kohnen and Nagaoka, which were later rederived by Haruki.
Versions
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BibTeX
@misc{takeda2026fourier,
title = {{Fourier Coefficients of Siegel-Eisenstein Series of Degree $2m$ and Weight $m+1$}},
author = {Nobuki Takeda},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.09136},
eprint = {2606.09136},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.09136},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fourier Coefficients of Siegel-Eisenstein Series of Degree 2m and Weight m+1
AU - Nobuki Takeda
PY - 2026
DA - 2026/06/09
PB - arXiv
DO - 10.48550/arxiv.2606.09136
UR - https://arxiv.org/abs/2606.09136
AB - We study Fourier coefficients of the Siegel-Eisenstein series E_m+1^(2m)(Z) for m≡1pmod4 and m≥5. Using the Fourier expansion formula due to Mizumoto, we determine the constant term and the exceptional non-zero Fourier coefficients. The result gives a higher-degree analogue of the degree-two formulas of Kohnen and Nagaoka, which were later rederived by Haruki.
ER -