Addendum to “Applications of differential algebra to algebraic independence of arithmetic functions” (Acta Arith. 172 (2016), 149–173)
Volume 196 / 2020
Acta Arithmetica 196 (2020), 325-327
MSC: Primary 11J85, 11A25, 13N15.
DOI: 10.4064/aa200210-14-7
Published online: 31 August 2020
Abstract
We give a version of Ax’s theorem for the ring of arithmetic functions without the assumption of continuity with respect to the norm of the derivations involved. Consequently, we obtain an unconditional generalization of the Jacobian criterion for algebraic independence of arithmetic functions.
