Equations in the Hadamard ring of rational functions
| dc.creator | Ferretti, Andrea | |
| dc.creator | Zannier, Umberto | |
| dc.date | 2007-01-26 | |
| dc.date.accessioned | 2026-07-07T07:43:20Z | |
| dc.date.available | 2026-07-07T07:43:20Z | |
| dc.description | Let k be a number field. It is well known that the set of sequences composed by Taylor coefficients of rational functions over k is closed under component-wise operations, and so it can be equipped with a ring structure. A conjecture due to Pisot asks if (after enlarging the field) one can take d-th roots in this ring, provided d-th roots of coefficients can be taken in k. This was proved true in a preceding paper of the second author; in this article we generalize this result to more general equations, monic in Y, where the former case can be recovered for g(X,Y)=X^d-Y=0. Combining this with the Hadamard quotient theorem by Pourchet and Van der Poorten, we are able to get rid of the monic restriction, and have a theorem that generalizes both results. | |
| dc.description | 18 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0701772 | |
| dc.identifier | http://arxiv.org/abs/math/0701772 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122783 | |
| dc.subject | Number Theory | |
| dc.subject | 11B37; 12E25; 13F25 | |
| dc.title | Equations in the Hadamard ring of rational functions | |
| dc.type | text |