1970•Proceedings of the National Academy of SciencesOpen access

A Differential Equation for an Eisenstein Series of Genus Two

Howard L. Resnikoff

Abstract

A nonlinear differential equation of order 8 satisfied by the Eisenstein series of weight 4 for Siegel's modular group of genus two is presented. This equation plays a role in the theory of modular functions of genus two similar to that played by the differential equation of the Weierstrass [unk]-function associated with elliptic curve.

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Key concepts: Eisenstein series, Modular form, Mathematics, Genus, Differential equation, Modular curve, Modular elliptic curve, Elliptic curve