权值2的爱森斯坦级数的导数和模对应的交点

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-04-27 DOI:10.1007/s12188-022-00256-4

Sungmun Cho, Shunsuke Yamana, Takuya Yamauchi

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引用次数: 1

摘要

我们给出了Siegel级数的某些值和导数的一个公式，并用它们来计算权重为2和亏格为3的Siegel-Essenstein级数的导数的傅立叶系数，这与3个算术模块对应关系的交集有关。应用包括对称矩阵的表示数的加权平均值之间的关系。

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Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences

We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight \(\frac{g}{2}\) and genus g. When \(g=4\), the Fourier coefficient is approximated by a certain Fourier coefficient of the central derivative of the Siegel Eisenstein series of weight 2 and genus 3, which is related to the intersection of 3 arithmetic modular correspondences. Applications include a relation between weighted averages of representation numbers of symmetric matrices.

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.