Abstract:

The original cyclic sum formula for multiple zeta values (MZVs) was first conjectured by M. Hoffman as a refinement of the classical sum formula. It was later proved by Ohno by introducing a type of multiple Dirichlet series. A variant of the cyclic sum formula is known for the multiple zeta star values (MZSV) and recently conjectured for symmetric multiple zeta values (SMZV). In this talk, I will give a general identity of hyperlogarithms in many variables which I call "Sandwiched cyclic sum formula", which can produce all these cyclic sum formulas as suitable limits of "thinest breads" cases. One of the significance is that the identity does not just unify the cyclic sum formulas for MZVs, MZSVz and SMZVs, but also produce a wide generalization to "thicker breads" case of each cyclic sum formula. This is a joint research work with Minoru Hirose at Kyushu University.