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4 papers · 1 filter
Integral points, divisibility between values of polynomials and entire curves on surfaces
Pietro Corvaja, Umberto Zannier
We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth…
Multidimensional continued fractions and a Minkowski function
Giovanni Panti
The Minkowski Question Mark function can be characterized as the unique homeomorphism of the real unit interval that conjugates the Farey map with the tent map. We construct an n-d…
A lower bound for the r-order of a matrix modulo N
Carlo Magagna
For a positive integer , we define the N-rank of a non singular integer matrix to be the maximum integer such that there exists a minor of order whose de…
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…