A proof of Pisot's dth root conjecture
| dc.creator | Zannier, Umberto | |
| dc.date | 2000-10-02 | |
| dc.date.accessioned | 2026-07-07T04:37:48Z | |
| dc.date.available | 2026-07-07T04:37:48Z | |
| dc.description | Let $\{b(n):n\in\N\}$ be the sequence of coefficients in the Taylor expansion of a rational function $R(X)\in\Q(X)$ and suppose that b(n) is a perfect $d^{\rm th}$ power for all large n. A conjecture of Pisot states that one can choose a $d^{\rm th}$ root a(n) of b(n) such that $\sum a(n)X^n$ is also a rational function. Actually, this is the fundamental case of an analogous statement formulated for fields more general than $\Q$. A number of papers have been devoted to various special cases. In this note we shall completely settle the general case. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010024 | |
| dc.identifier | http://arxiv.org/abs/math/0010024 | |
| dc.identifier | Ann. of Math. (2) 151 (2000), no. 1, 375--383 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60038 | |
| dc.subject | Number Theory | |
| dc.subject | 11Rxx (11Bxx) | |
| dc.title | A proof of Pisot's dth root conjecture | |
| dc.type | text |