PreprintCC BY 4.0arXiv
On the Space Defined by the Modular Transformation Law for Multiple Eisenstein Series
Abstract
Motivated by a modular transformation law for multiple Eisenstein series established by Yu, we introduce spaces of holomorphic functions satisfying this law together with an additional filtration condition. We show that these spaces contain the spaces spanned by admissible multiple Eisenstein series, are finitedimensional in each weight, and share several structural properties with them. We also obtain an explicit formula for the generating function of their dimensions. However, the inclusions are known to be strict for certain weights. Thus, the defining conditions do not suffice to characterize the spaces spanned by admissible multiple Eisenstein series.
Related
- Lie algebras for multiple Eisenstein series and multiple q-zeta values
- Modularity criteria for multiple Eisenstein series
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- On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
- The sl2-algebra structure of multiple Eisenstein series
BibTeX
@misc{kina2026space,
title = {{On the Space Defined by the Modular Transformation Law for Multiple Eisenstein Series}},
author = {Katsumi Kina},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02331},
eprint = {2611.02331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02331},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Space Defined by the Modular Transformation Law for Multiple Eisenstein Series
AU - Katsumi Kina
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02331
UR - https://arxiv.org/abs/2611.02331
AB - Motivated by a modular transformation law for multiple Eisenstein series established by Yu, we introduce spaces of holomorphic functions satisfying this law together with an additional filtration condition. We show that these spaces contain the spaces spanned by admissible multiple Eisenstein series, are finitedimensional in each weight, and share several structural properties with them. We also obtain an explicit formula for the generating function of their dimensions. However, the inclusions are known to be strict for certain weights. Thus, the defining conditions do not suffice to characterize the spaces spanned by admissible multiple Eisenstein series.
ER -