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arXiv · 2609.03777

The $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein series

Henrik Bachmann·Hayato Kanno
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Abstract

We prove that the algebra of multiple Eisenstein series is an $\mathfrak{sl}_2$-algebra. In particular, we show that it is graded by weight, which also holds after taking complex linear spans. Further, we identify it as a graded $\mathbb{Q}$-algebra with the associated graded algebra of $q$-analogues of multiple zeta values with respect to the weight filtration. The main ingredient is an estimate that compares the usual defining sums of multiple Eisenstein series with sums over a lattice order depending on an integer $N$.

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Henrik Bachmann, Hayato Kanno. 2026-09-03. The $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein series. https://arxiv.org/abs/2609.03777

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