Hyperderivatives of the deformation series associated with arithmetic gamma values and characteristic $p$ multiple zeta values
Number Theory
2024-10-31 v2
Abstract
In the number theory in positive characteristic, there are analogues of some special values introduced by Carlitz, Carlitz gamma values and Carlitz zeta values for instance. Each of them is further developed to arithmetic gamma values and multiple zeta values by Goss and Thakur respectively. In this paper, by generalizing a result of Chang-Papanikolas-Thakur-Yu (2010), we obtain the algebraic independence of certain arithmetic gamma values, positive characteristic multiple zeta values of restricted indices and hyperderivatives of their deformations. We prove this by using Chang-Papanikolas-Yu's derivation, Maurichat's prolongation, Namoijam's formula and Papanikolas' theory of -motivic Galois group.
Keywords
Cite
@article{arxiv.2408.10730,
title = {Hyperderivatives of the deformation series associated with arithmetic gamma values and characteristic $p$ multiple zeta values},
author = {Ryotaro Harada and Daichi Matsuzuki},
journal= {arXiv preprint arXiv:2408.10730},
year = {2024}
}