Common divisors of a^n-1 and b^n-1 over function fields
| dc.creator | Silverman, Joseph H. | |
| dc.date | 2004-01-26 | |
| dc.date.accessioned | 2026-07-07T05:04:52Z | |
| dc.date.available | 2026-07-07T05:04:52Z | |
| dc.description | Ailon and Rudnick have shown that if $a,b \in C[T]$ are multiplicatively independent polynomials, then $°(\gcd(a^n-1,b^n-1))$ is bounded for all $n\ge1$. We show that if instead $a,b \in F[T]$ for a finite field $F$ of characteristic $p$, then $°(\gcd(a^n-1,b^n-1))$ is larger than $Cn$ for a constant $C=C(a,b)>0$ and for infinitely many $n$, even if $n$ is restricted in various reasonable ways (e.g., $gec(n,p)=1$). | |
| dc.identifier | https://arxiv.org/abs/math/0401356 | |
| dc.identifier | http://arxiv.org/abs/math/0401356 | |
| dc.identifier | New York Journal of Math. (electronic) 10 (2004), 37--43 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69974 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11T55; 11R58; 11D61 | |
| dc.title | Common divisors of a^n-1 and b^n-1 over function fields | |
| dc.type | text |