Hyperderivatives of the deformation series associated with arithmetic gamma values and characteristic p multiple zeta values

2024/08/20 by Ryotaro Harada, Harada, Ryotaro, Daichi Matsuzuki +1
Materials Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Crystallization and Solubility Studies #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.10730

openalex publication_date 2024/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 t-motivic Galois group.

Related

• Multiple zeta values with varying constant fields
• On algebraic independence of Taylor coefficients of certain Anderson-Thakur series
• Zagier-Hoffman's conjectures in positive characteristic
• Hopf algebras and multiple zeta values in positive characteristic
• A new deformation of multiple zeta value