Powers with second differences equal to 2.


Natalia Garcia-Fritz ( University of Toronto, Canada )
2016-05-13  10:30 - 11:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk we will show that if we fix an integer k>2, then the Bombieri-Lang conjecture for surfaces implies that sequences of rational k-th powers with second differences equal to 2 have length bounded only in terms of k. We do this by finding all the curves of genus 0 or 1 on certain general type surfaces associated to this problem, and this is done by an extension of a method implicit in work of Vojta (for the case k=2). We also study the existence of a bound in the case of powers with different exponents under the 4 term ABC conjecture.