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

2015/03/03 by Tomoya Machide, Machide, Tomoya · 1 citation
Mathematics · #11M32(Primary) #16S34 #20C07(Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1503.01194

openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we prove an identity for the generating function of the\nquadruple zeta values. Taking homogeneous parts on both sides of the identity\nand substituting appropriate values for the variables, we obtain the sum\nformula for quadruple zeta values. We also obtain its weighted analogues, which\ninclude the formulas for this case proved by Guo and Xie (2009, J. Number\nTheory 129, 2747--2765) and by Ong, Eie, and Liaw (2013, Int. J. Number Theory\n9, 1185--1198).\n

Citations

• A parameterized generalization of the sum formula for quadruple zeta values

Cited by

• Yamamoto's interpolation of finite multiple zeta and zeta-star values

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