Number Theory Seminar FS 2017

Unless otherwise stated, all talks start at 14.15 and take place in seminar room 00.003, Spiegelgasse 1

Information for speakers

02.03.2017Igor Shparlinksi (Univ. of New South Wales/MPI-Bonn)Multiplicatively dependent algebraic numbers(joint work with Alina Ostafe, Francesco Pappalardi, Min Sha, Cam Stewart) We discuss various questions related to the distribution of vectors of algebraic numbers (u_1, …., u_n) which are multiplicatively dependent. In particular, we present some counting results for the number of such vectors of degree d and height h (from a fixed number field K and from Q-bar). We also give both sided estimates on their density in R^n. Finally we give an analogue of a result of Bombieri-Masser-Zannier (1999) proving the boundedness of the “house" of the shifts v from the abelian closure of a given number field K, for which the vector (u_1-v, …., u_n-v) becomes multiplicatively dependent, rather than the boundedness of their height as in BMZ’99 (but for shifts v from Q-bar). This result has applications to multiplicative dependence in orbits of polynomial dynamical systems, generalising those on roots of unity.
06.04.2017Yuri Bilu
18.05.2017Gabino Gonzales Diez (Univ. Auto. de Madrid)