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Applications of differential algebra to algebraic independence of arithmetic functions

Volume 172 / 2016

Wai Yan Pong Acta Arithmetica 172 (2016), 149-173 MSC: Primary 11J85, 11A25, 12H05; Secondary 11J91, 11J72. DOI: 10.4064/aa8112-12-2015 Published online: 3 December 2015


We generalize and unify the proofs of several results on algebraic independence of arithmetic functions and Dirichlet series by using a theorem of Ax on the differential Schanuel conjecture. Along the way, we find counter-examples to some results in the literature.


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

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