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The sl2-algebra structure of multiple Eisenstein series
Abstract
We prove that the algebra of multiple Eisenstein series is an sl2-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 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.
Related
- Lie algebras for multiple Eisenstein series and multiple q-zeta values
- Modularity criteria for multiple Eisenstein series
- Zagier's 2-3-2 formula for multiple Eisenstein series
- On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
- On the Space Defined by the Modular Transformation Law for Multiple Eisenstein Series
BibTeX
@misc{bachmann2026sl2algebra,
title = {{The $\mathfraksl_2$-algebra structure of multiple Eisenstein series}},
author = {Henrik Bachmann and Hayato Kanno},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03777},
eprint = {2609.03777},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03777},
}
RIS
TY - UNPB
TI - The sl_2-algebra structure of multiple Eisenstein series
AU - Henrik Bachmann
AU - Hayato Kanno
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03777
UR - https://arxiv.org/abs/2609.03777
AB - We prove that the algebra of multiple Eisenstein series is an 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 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.
ER -