A parameterized generalization of the sum formula for quadruple zeta values

Abstract

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also obtain weighted sum formulas for quadruple zeta values, which contain some known results.

Use of the generating function to generalize the sum formula for quadruple zeta values

“…REMARK 1.3. Theorem 1.1 and Corollary 1.2 in the present paper are expansions of Theorems 1.1 and 1.2 in [12], respectively; the results that will be stated below are expansions of the results following Section 2.1 in [12]. The results of Section 2.1 have been amplified in [16].…”

Identities involving cyclic sums of regularized multiple zeta values each of depth less than $5$

“…We recommend that, on first reading, those readers who are interested only in the ideas skip over the statements relating to the proof of (1.3) (or statements in the case of depth 4). (ii) The present paper is an expansion of Section 2.1 in [9]. The remainder of the results of [9] will be amplified in a forthcoming paper [10].…”

“…(ii) The present paper is an expansion of Section 2.1 in [9]. The remainder of the results of [9] will be amplified in a forthcoming paper [10].…”