Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences
Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences
复制标题
权重 2 的爱森斯坦级数的导数和模对应的交集
DOI：
10.1007/s12188-022-00256-4
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发表时间：
2022
影响因子：
0.4
通讯作者：
Takuya Yamauchi
中科院分区：
文献类型：
--
作者：
Sungmun Cho;Shunsuke Yamana;Takuya Yamauchi
给出了Siegel级数某些值和导数的一个公式，并用它们计算了Siegel Eisenstein级数的导数的傅里叶系数。当，傅里叶系数由权为2且亏格为3的Siegel Eisenstein级数的中心导数的某个傅立叶系数来近似时，这与3个算术模对应的交集有关。应用包括对称矩阵的表示数的加权平均值之间的关系。
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 weightand genusg. When, 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.