Posted in

Speaker:

Alina Ostafe
Affiliation:

University of New South Wales/MPIM
Date:

Tue, 10/03/2020 - 14:00 - 15:00
Location:

MPIM Lecture Hall
Parent event:

Seminar on Algebra, Geometry and Physics Let $a,b$ be multiplicatively independent positive integers and $\varepsilon>0$. Bugeaud, Corvaja and Zannier (2003)

proved that $\gcd(a^n-1,b^n-1)\le \exp(\varepsilon n)$ for sufficiently large $n$. Ailon and Rudnick (2004) considered

the function field analogue and proved a much stronger result. In this talk we present several extensions of the result of

Ailon and Rudnick. We also look at some gcd problems for linear recurrence sequences, posing some open questions,

and if time allows on compositional iterates of univariate polynomials.

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