Year: 2026
Type: preprint
Abstract: We prove a multiple Eisenstein series analogue of Zagier's formula for the multiple zeta values $ζ(2,\ldots,2,3,2,\ldots,2)$. 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 $\mathfrak{sl}_2$-structure and a modularity criterion of Yu to prove the identity by induction.
Source: arXiv (Cornell University)
Author: Bachmann, Henrik
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222923667