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Addendum to “Applications of differential algebra to algebraic independence of arithmetic functions” (Acta Arith. 172 (2016), 149–173)

Volume 196 / 2020

Wai Yan Pong Acta Arithmetica 196 (2020), 325-327 MSC: Primary 11J85, 11A25, 13N15. DOI: 10.4064/aa200210-14-7 Published 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.


  • Wai Yan PongCalifornia State University Dominguez Hills
    1000 E Victoria Street
    Carson, CA 90747, U.S.A.

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