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Mathematics > Number Theory

arXiv:1805.01666 (math)
[Submitted on 4 May 2018 (v1), last revised 18 Apr 2020 (this version, v2)]

Title:A reformulation of the Siegel series and intersection numbers

Authors:Sungmun Cho, Takuya Yamauchi
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Abstract:In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multiplicities of [GK93] and the Siegel series have the same inherent structures, beyond matching values. As an application, we will prove a new identity between the intersection number of two modular correspondences over Fp and the sum of the Fourier coefficients of the Siegel-Eisenstein series for Sp_4 of weight 2, which is independent of p (> 2). In addition, we will explain a description of the local intersection multiplicities of the special cycles over F_p on the supersingular locus of the `special fiber' of the Shimura varieties for GSpin(n; 2), n<=3 in terms of the Siegel series directly.
Comments: 52 pages
Subjects: Number Theory (math.NT)
MSC classes: 11F30, 11F46, 11G18, 14C17, 14G35, 14J15
Cite as: arXiv:1805.01666 [math.NT]
  (or arXiv:1805.01666v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.01666

Submission history

From: Sungmun Cho [view email]
[v1] Fri, 4 May 2018 08:51:17 UTC (54 KB)
[v2] Sat, 18 Apr 2020 09:36:49 UTC (63 KB)
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