PreprintCC BY 4.0arXiv
Refined sum formulas for finite multiple zeta values of level two
Abstract
In this paper, we establish two classes of refined sum formulas for finite multiple zeta values of level two, a variant of finite multiple zeta values recently introduced by M. Kaneko et al. One is an explicit formula for the sum of level-two finite multiple zeta values over indices in which one prescribed component is odd and all the remaining components are even. The other is an Ohno--Zagier type relation for level-two finite multiple zeta values, which gives a generating function for sums of fixed weight, depth and height in terms of depth-one values. As applications, we derive sum formulas for fixed weight and depth and for several special heights.
Related
- Weighted sum formulas for finite multiple mixed values
- Duality formulas for 𝒬̂-multiple zeta values
- Lower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta values
- A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral 2H2 summation
- Formal finite multiple zeta values
BibTeX
@misc{wang2026refined,
title = {{Refined sum formulas for finite multiple zeta values of level two}},
author = {Zhenlu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23562},
eprint = {2609.23562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23562},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Refined sum formulas for finite multiple zeta values of level two
AU - Zhenlu Wang
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23562
UR - https://arxiv.org/abs/2609.23562
AB - In this paper, we establish two classes of refined sum formulas for finite multiple zeta values of level two, a variant of finite multiple zeta values recently introduced by M. Kaneko et al. One is an explicit formula for the sum of level-two finite multiple zeta values over indices in which one prescribed component is odd and all the remaining components are even. The other is an Ohno--Zagier type relation for level-two finite multiple zeta values, which gives a generating function for sums of fixed weight, depth and height in terms of depth-one values. As applications, we derive sum formulas for fixed weight and depth and for several special heights.
ER -