PreprintCC BY 4.0arXiv
Zagier's 2-3-2 formula for multiple Eisenstein series
Abstract
We prove a multiple Eisenstein series analogue of Zagier's formula for the multiple zeta values ζ(2,…,2,3,2,…,2). The multiple Eisenstein series identity contains correction terms given by derivatives of odd Eisenstein series. Using the Goncharov coproduct and Brown's motivic version of Zagier's formula, we show that the normalized difference has rational Fourier coefficients. We then use the sl2-structure and a modularity criterion of Yu to prove the identity by induction.
Related
- Lie algebras for multiple Eisenstein series and multiple q-zeta values
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- The sl2-algebra structure of multiple Eisenstein series
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BibTeX
@misc{bachmann2026zagiers,
title = {{Zagier's 2-3-2 formula for multiple Eisenstein series}},
author = {Henrik Bachmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23052},
eprint = {2610.23052},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23052},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zagier's 2-3-2 formula for multiple Eisenstein series
AU - Henrik Bachmann
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23052
UR - https://arxiv.org/abs/2610.23052
AB - We prove a multiple Eisenstein series analogue of Zagier's formula for the multiple zeta values ζ(2,…,2,3,2,…,2). The multiple Eisenstein series identity contains correction terms given by derivatives of odd Eisenstein series. Using the Goncharov coproduct and Brown's motivic version of Zagier's formula, we show that the normalized difference has rational Fourier coefficients. We then use the sl_2-structure and a modularity criterion of Yu to prove the identity by induction.
ER -