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arXiv · 2607.27702

Schur Eisenstein series and Schur MacMahon series

Henrik Bachmann·Jinbo Yu
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Abstract

We introduce and study two partition-indexed families of quasimodular forms obtained from Schur functions: Schur Eisenstein series and Schur MacMahon series. An explicit transition between them can be interpreted as a convolution in a Fa\`a di Bruno Hopf algebra of symmetric functions. We discuss the classical sl2-action and prove that Schur Eisenstein series for partitions with parts of size at most 3 give a basis for quasimodular forms. Further, we conjecture that the Schur MacMahon series span all quasimodular forms with integral coefficients.

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Henrik Bachmann, Jinbo Yu. 2026-07-30. Schur Eisenstein series and Schur MacMahon series. https://arxiv.org/abs/2607.27702

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