Thomas’ conjecture over function fields
Thomas’ conjecture is, given monic polynomials
Thomas’ conjecture is, given monic polynomials
It is proved that for every k there exist k triples of positive integers with the same sum and the same product.
In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.