Applications of differential algebra to algebraic independence of arithmetic functions
Volume 172 / 2016
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
Abstract
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.
