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

2018/02/17 by Sungmun Cho, Shunsuke Yamana, Cho, Sungmun +3
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1802.06273

openalex publication_date 2018/02/17 · openalex created_date 2018/03/06 · openalex updated_date 2026/07/28

Abstract

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 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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