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

Abstract Number theory for positive characteristic contains analogues of the special values that were introduced by Carlitz; these include the Carlitz gamma values and Carlitz zeta values. These values were further developed to the arithmetic gamma values and multiple zeta values by Goss and Thakur, respectively. In this work, by generalizing a result attained by Chang et al., we obtain the algebraic independence of arithmetic gamma values, positive characteristic multiple zeta values of restricted indices, and the hyperderivatives of their deformations. We prove this by using Chang–Papanikolas–Yu's derivation, Maurichat's prolongation, Namoijam's formula, and Papanikolas' theory of the ‐motivic Galois group.