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