Catalogue of modular relations for double zeta values

Abstract

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated' from modular forms on (a subgroup of) the full modular group. Several kinds of such relations, in particular, for double zeta values have been found up to now. It is our purpose to review these results and also succinctly outline potential avenues for future research projects.