Addendum to “Applications of differential algebra to algebraic independence of arithmetic functions” (Acta Arith. 172 (2016), 149–173)
Tom 196 / 2020
Acta Arithmetica 196 (2020), 325-327 MSC: Primary 11J85, 11A25, 13N15. DOI: 10.4064/aa200210-14-7 Opublikowany online: 31 August 2020
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.