Applications of differential algebra to algebraic independence of arithmetic functions
Wai Yan Pong
Acta Arithmetica, Tome 172 (2016), p. 149-173 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:279683 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8112-12-2015,
     author = {Wai Yan Pong},
     title = {Applications of differential algebra to algebraic independence of arithmetic functions},
     journal = {Acta Arithmetica},
     volume = {172},
     year = {2016},
     pages = {149-173},
     zbl = {06545345},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8112-12-2015}
}

Wai Yan Pong. Applications of differential algebra to algebraic independence of arithmetic functions. Acta Arithmetica, Tome 172 (2016) pp. 149-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8112-12-2015/