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Modularity criteria for multiple Eisenstein series
Abstract
We give two criteria for a linear combination of multiple Eisenstein series of fixed weight to be a modular form, one in terms of its Fourier coefficients and one in terms of its L-function. The first criterion follows from an exact transformation formula under SL2(ℤ), which describes the modular defect of multiple Eisenstein series explicitly. The second criterion is a Hecke converse theorem for multiple Eisenstein series, which shows that the functional equation of the L-function alone already implies modularity.
Related
- Lie algebras for multiple Eisenstein series and multiple q-zeta values
- Zagier's 2-3-2 formula for multiple Eisenstein series
- On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
- The sl2-algebra structure of multiple Eisenstein series
- On the Space Defined by the Modular Transformation Law for Multiple Eisenstein Series
BibTeX
@misc{yu2026modularity,
title = {{Modularity criteria for multiple Eisenstein series}},
author = {Jinbo Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21291},
eprint = {2610.21291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21291},
}
RIS
TY - UNPB
TI - Modularity criteria for multiple Eisenstein series
AU - Jinbo Yu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21291
UR - https://arxiv.org/abs/2610.21291
AB - We give two criteria for a linear combination of multiple Eisenstein series of fixed weight to be a modular form, one in terms of its Fourier coefficients and one in terms of its L-function. The first criterion follows from an exact transformation formula under SL_2(ℤ), which describes the modular defect of multiple Eisenstein series explicitly. The second criterion is a Hecke converse theorem for multiple Eisenstein series, which shows that the functional equation of the L-function alone already implies modularity.
ER -