COLLOQUIO DE GIORGI
Yuri Bilu
Universitè de Bordeaux I
"Diophantine equations with separated variables"
We describe pairs (f,g) of polynomials with rational coefficients such that the equation f(x)=g(y) has infinitely many solutions in integers x,y. Using classical results of Siegel and Ritt, together with some ideas of M. Fried, we show that, up to a linear change of variables, any such pair is of the form f(x) = h(u(x)) and g(y) = h(v(y)), where u,v are polynomials of very particular form and h is an arbitrary polynomial with rational coefficients.
Martedì 21 febbraio 2006
ore 17.00
Aula Mancini
Piazza dei Cavalieri, 7
PISA
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