### Abstract

We define polynomials of one variable t whose values at t = 0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the sum formula and the cyclic sum formula for these polynomials.

Original language | English |
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Pages (from-to) | 102-114 |

Number of pages | 13 |

Journal | Journal of Algebra |

Volume | 385 |

DOIs | |

Publication status | Published - 2013 Jul 1 |

### Fingerprint

### Keywords

- Cyclic sum formula
- Multiple zeta values
- Multiple zeta-star values
- Sum formula
- Two-one conjecture

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*385*, 102-114. https://doi.org/10.1016/j.jalgebra.2013.03.023

**Interpolation of multiple zeta and zeta-star values.** / Yamamoto, Shuji.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 385, pp. 102-114. https://doi.org/10.1016/j.jalgebra.2013.03.023

}

TY - JOUR

T1 - Interpolation of multiple zeta and zeta-star values

AU - Yamamoto, Shuji

PY - 2013/7/1

Y1 - 2013/7/1

N2 - We define polynomials of one variable t whose values at t = 0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the sum formula and the cyclic sum formula for these polynomials.

AB - We define polynomials of one variable t whose values at t = 0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the sum formula and the cyclic sum formula for these polynomials.

KW - Cyclic sum formula

KW - Multiple zeta values

KW - Multiple zeta-star values

KW - Sum formula

KW - Two-one conjecture

UR - http://www.scopus.com/inward/record.url?scp=84876475543&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876475543&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2013.03.023

DO - 10.1016/j.jalgebra.2013.03.023

M3 - Article

VL - 385

SP - 102

EP - 114

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -