Generating functions for sums of polynomial multiple zeta values
Minoru Hirose, Hideki Murahara, Shingo Saito

TL;DR
This paper introduces generating functions for polynomial multiple zeta values, revealing their connection to sum formulas and symmetric variants, and unifies these concepts through identities involving Schur multiple zeta values.
Contribution
It provides a new generating function approach that generalizes sum formulas for multiple zeta values and their symmetric counterparts, linking them via Schur multiple zeta values.
Findings
Derived sum formulas for polynomial multiple zeta(-star) values
Unified sum formulas for multiple zeta and symmetric multiple zeta values
Established identities involving Schur multiple zeta values
Abstract
The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta values. We also obtain the sum formula for polynomial multiple zeta(-star) values in terms of generating functions, simultaneously generalizing the sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Drug Solubulity and Delivery Systems
