Cone multiple zeta values, Shintani multiple zeta values and their double subdivision relations

Meeting Details

Abstract: This is a geometric approach to study relations among Shintani multiple zeta values. We introduce (open/closed) cone multiple zeta values as the bridge to explore Shintani multiple zeta values geometrically, and show that they span the same linear spaces over $\Q$. We then show the linear space of simple fractions and the linear space spanned by cones (modulo subdivisions) are isomorphic. Therefore Shintani multiple zeta values carry two sets of relations (double subdivision relations) from subdivision of open and closed cones. This double subdivision relations generalize the double shuffle relations of multiple zeta values. This is joint work with L. Guo and S. Paycha.