PreprintCC BY 4.0arXiv
A Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated Integrals
Abstract
We introduce a formal multiple polylogarithm function (FMPF) and general formal Arakawa-Kaneko zeta values (GFAKZVs), and establish several useful properties analogous to those of the ordinary Arakawa-Kaneko zeta values by employing the method of iterated integrals, a powerful tool originating in algebraic topology. In particular, we prove various duality and sum formulas involving FMPFs and GFAKZVs. This allows us to derive, in a uniform manner, a number of known results concerning Arakawa-Kaneko zeta values and Kaneko-Tsumura ψ-values that were previously obtained by different approaches, thereby highlighting the unifying power of the iterated integral formalism.
Related
- Iterated cotangent-difference integrals over totally real cyclotomic fields
- Iterated integrals for generalized Appell functions
- Distribution of Kaneko's val function
- Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture
- Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras
BibTeX
@misc{pan2026unified,
title = {{A Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated Integrals}},
author = {Ende Pan and Ce Xu and Jianqiang Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33019},
eprint = {2609.33019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33019},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated Integrals
AU - Ende Pan
AU - Ce Xu
AU - Jianqiang Zhao
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.33019
UR - https://arxiv.org/abs/2609.33019
AB - We introduce a formal multiple polylogarithm function (FMPF) and general formal Arakawa-Kaneko zeta values (GFAKZVs), and establish several useful properties analogous to those of the ordinary Arakawa-Kaneko zeta values by employing the method of iterated integrals, a powerful tool originating in algebraic topology. In particular, we prove various duality and sum formulas involving FMPFs and GFAKZVs. This allows us to derive, in a uniform manner, a number of known results concerning Arakawa-Kaneko zeta values and Kaneko-Tsumura ψ-values that were previously obtained by different approaches, thereby highlighting the unifying power of the iterated integral formalism.
ER -