Equidistribution and integral points for Drinfeld modules

Dragos Ghioca, Thomas J. Tucker

Published 2006-09-05, updated 2007-04-11Version 2

We prove that the local height of a point on a Drinfeld module can be computed by averaging the logarithm of the distance to that point over the torsion points of the module. This gives rise to a Drinfeld module analog of a weak version of Siegel's integral points theorem over number fields and to an analog of a theorem of Schinzel's regarding the order of a point modulo certain primes.