Sum of multiple $q$-zeta values

Li, Zhonghua

doi:10.1090/s0002-9939-09-10096-5

Cited by 8 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [1,2], T. Aoki, Y. Kombu and Y. Ohno expressed a generating function of sums of MZSVs of fixed weight, depth and height by hypergeometric functions and obtained some relations of MZSVs. We discussed sum of MZVs of fixed weight, depth and i-height in [14], and obtained its q-analogue in [15]. And T. Aoki, Y. Ohno and N. Wakabayashi studied the sums of MZSVs of fixed weight, depth and i-height in [3].…”

Section: Introductionmentioning

confidence: 99%

Some relations of interpolated multiple zeta values

Chen

2017

Int. J. Math.

View full text Add to dashboard Cite

Abstract. In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums of interpolated multiple zeta values of fixed weight, depth and height is represented by hypergeometric functions, and we discuss some special cases.

show abstract

Section: Introductionmentioning

confidence: 99%

Some relations of interpolated multiple zeta values

Chen

2017

Int. J. Math.

View full text Add to dashboard Cite

show abstract

“…The proof of Theorem 1.1 is similar to that of other Ohno-Zagier type relations [1,3,[5][6][7]. We first study a similar sum of the interpolated finite q-multiple polylogarithms in this section.…”

Section: Sum Of Interpolated Finite Q-multiple Polylogarithmsmentioning

confidence: 88%

Sum of interpolated finite multiple harmonic q-series

Pan

2019

Journal of Number Theory

View full text Add to dashboard Cite

We define and study the interpolated finite multiple harmonic q-series. A generating function of the sums of the interpolated finite multiple harmonic qseries with fixed weight, depth and i-height is computed. Some Ohno-Zagier type relation with corollaries and some evaluation formulas of the interpolated finite multiple harmonic q-series at roots of unity are given.respectively. Here for any m ∈ N, [m] is the q-integer [m] = 1−q m 1−q . It was proved in [2, Theorems 1.1, 1.2] that the values z n (k; ζ n ) and z ⋆ n (k; ζ n ) closely relate to the finite and the symmetric multiple zeta (star) values, where ζ n is a fixed primitive n-th root of unity. Motivated by these observations, the authors of [2] gave a re-interpretation of *

show abstract

“…When t = 0 our main theorem reduces to the result in Li [7] as follows. Note that, in the case of t = 0,…”

Section: The Case Of T =mentioning

confidence: 95%

“…Proof of Lemma 16. This identity holds when t = 0 according to (7) in Okuda-Takeyama [10]. Let L be the Q[t]-linear map given by…”

Section: T-qmzvs As Special Values Of T-qmplsmentioning

confidence: 99%

See 1 more Smart Citation

Sum of interpolated multiple q-zeta values

Wakabayashi

2019

Journal of Number Theory

View full text Add to dashboard Cite

Interpolated multiple q-zeta values are deformation of multiple q-zeta values with one parameter, t, and restore classical multiple zeta values as t = 0 and q → 1. In this paper, we discuss generating functions for sum of interpolated multiple q-zeta values with fixed weight, depth and i-height. The functions are systematically expressed in terms of the basic hypergeometric functions. Compared with the result of Ohno and Zagier, our result includes three generalizations: general height, q-deformation and t-interpolation. As an application, we prove some expected relations for interpolated multiple q-zeta values including sum formulas.

show abstract

Sum of multiple $q$-zeta values

Abstract: Abstract. The generating function of the sums of multiple q-zeta values with fixed weights, depths and 1-heights, 2-heights, . . . , r-heights is represented in terms of specializations of basic hypergeometric functions.

Cited by 8 publications

References 9 publications

Some relations of interpolated multiple zeta values

Some relations of interpolated multiple zeta values

Sum of interpolated finite multiple harmonic q-series

Sum of interpolated multiple q-zeta values

Contact Info

Product

Resources

About