RÉSUMÉ

This is joint work with Thomas Loher. Let K be a number field of degree d. We estimate the number of points over K with height at most T>=1. A typical result is that there are at most (1088.d.log(d))^n.T^((n+1).d) vectors a=(a1,...,an) in K^n with absolute (non logarithmic) height H(a) lower or equal to T, provided d<>1. This improves earlier work of Evertse and Schmidt. The exponent (n+1)d is sharp (by a classical theorem of Schannel) and the factors log(d) cannot be removed.

WWW page design par Thomas Papanikolaou & Christine Bachoc