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Greatest common divisors of u - 1 , v - 1 in positive characteristic and rational points on curves over finite fields

Pietro Corvaja, Umberto Zannier (2013)

Journal of the European Mathematical Society

In our previous work we proved a bound for the g c d ( u 1 , v 1 ) , for S -units u , v of a function field in characteristic zero. This generalized an analogous bound holding over number fields, proved in [3]. As pointed out by Silverman, the exact analogue does not work for function fields in positive characteristic. In the present work, we investigate possible extensions in that direction; it turns out that under suitable assumptions some of the results still hold. For instance we prove Theorems 2 and 3 below, from...

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