Year: 2026
Type: preprint
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 $N$.
Source: arXiv (Cornell University)
Authors: Bachmann, Henrik, Kanno, Hayato
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208751549