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

2019/08/25 by Hideki Murahara, Murahara, Hideki, Masataka Ono +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11M32 #Secondary 05A19

paper · pdf · doi:10.48550/arxiv.1908.09307

openalex publication_date 2019/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable t, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in particular, prove the cyclic sum formula, the Bowman-Bradley type formula, and the weighted sum formula. The harmonic relation, the shuffle relation, the duality relation, and the derivation relation are also presented.

Citations

• Use of the generating function to generalize the sum formula for\n quadruple zeta values
• On variants of symmetric multiple zeta-star values and the cyclic sum formula

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• Interpolation of multiple zeta and zeta-star values
• Ohno-type relation for interpolated multiple zeta values
• Algebraic relations of interpolated multiple zeta values
• Interpolation of q-analogue of multiple zeta and zeta-star values
• Interpolated polynomial multiple zeta values of fixed weight, depth, and height