University of Cambridge > Talks.cam > Number Theory Seminar > On some unlikely intersections for values and orbits of rational functions

On some unlikely intersections for values and orbits of rational functions

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  • UserAlina Ostafe (The University of New South Wales)
  • ClockTuesday 18 February 2020, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jessica Fintzen.

For given rational functions f_1, ... ,f_s defined over a number field K, Bombieri, Masser and Zannier (1999) proved that the algebraic numbers alpha for which the values f_1(alpha),... , f_s(alpha) are multiplicatively dependent are of bounded height (unless this is false for an obvious reason).

Motivated by this, we present recent finiteness results on multiplicative relations of values of rational functions at arguments restricted to the maximal abelian extension of K. We go even further and discuss the presence of multiplicative relations modulo finitely generated groups, posing some open questions. If time allows, we will present some finiteness results regarding the presence of powers of S-integers in orbits of polynomial dynamical systems.

This talk is part of the Number Theory Seminar series.

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