2 citations · 4 across the 5 of their papers we have counts for
6 papers
On the rational approximations to the powers of an algebraic number
Pietro Corvaja, Umberto Zannier
About fifty years ago Mahler proved that if is rational but not an integer and if then the fractional part of is apart from a finite set of integers …
On the length of continued fractions for values of quotients of power sums
Pietro Corvaja, Umberto Zannier
Generalizing a result of Pourchet, we prove that, if are power sums satisfying suitable conditions, the length of the continued fraction of the ratio tends to inf…
A lower bound for the height of a rational function at -unit points
Pietro Corvaja, Umberto Zannier
Let be a finitely generated subgroup of the multiplicative group $\G_m^2(\bar{Q})$. Let $p(X,Y),q(X,Y)\in\bat{Q}$ be two coprime polynomials not both vanishing at ; let…
On integral points on surfaces
Pietro Corvaja, Umberto Zannier
We study integral points on affine surfaces by means of a new method, relying on the Subspace Theorem. Under suitable assumptions on the divisor at infinity, we prove that the inte…
On the greatest prime factor of (ab+1)(ac+1)
Pietro Corvaja, Umberto Zannier
We prove that for integers a>b>c>0, the greatest prime factor of (ab+1)(ac+1) tends to infinity with a.
A proof of Pisot's dth root conjecture
Umberto Zannier
Let 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 power for all la…