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- W2953071462 abstract "In this paper we present some extensions of the Ailon-Rudnick Theorem, which says that if $f,gin{mathbb C}[T]$, then $gcd(f^n-1,g^m-1)$ is bounded for all $n,mge 1$. More precisely, using a uniform bound for the number of torsion points on curves and results on the intersection of curves with algebraic subgroups of codimension at least $2$, we present two such extensions in the univariate case. We also give two multivariate analogues of the Ailon-Rudnick Theorem based on Hilbert's irreducibility theorem and a result of Granville and Rudnick about torsion points on hypersurfaces." @default.
- W2953071462 created "2019-06-27" @default.
- W2953071462 creator A5008253632 @default.
- W2953071462 date "2015-05-15" @default.
- W2953071462 modified "2023-09-27" @default.
- W2953071462 title "On some extensions of the Ailon-Rudnick Theorem" @default.
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