On the Borisov-Gunnells relations for products of Eisenstein series

Abstract

Borisov and Gunnells have proved that certain linear combinations of products of Eisenstein series are Eisenstein series themselves, in analogy with the Manin relations for modular symbols. We devise a new method for determining and proving such relations, by differentiating with respect to the parameters of the Eisenstein series.

10 pages. v2: I expanded the introduction, clarified some arguments and added a final section with open questions