Overdetermined systems of lacunary equations (joint work with L. Leroux and M. Sombra) (40')
speaker: Francesco Amoroso (Université de Caen Basse-Normandie)abstract: Let f, g be polynomials of degree at most d of bounded height and having a bounded number of non zero coefficients. Assuming that at least one of f and g does not vanish at roots of unity, Filaseta, Granville and Schinzel proved that there exists an algorithm which compute the greatest common divisor of f and g in O(log d) arithmetic operations. This result heavily relies on a work of Bombieri and Zannier on the intersection of a subvariety of Gmn of codimension 2 with subgroups of dimension 1, which is in turn a special case of a celebrated conjecture of Zilber. Assuming an effective version of the full Zilber conjecture, we provide a generalization of the algorithm of Filaseta, Granville and Schinzel to overdetermined systems of lacunary equations in several variables.
timetable:
Tue 9 Oct, 10:30 - 11:10, Sala Conferenze Centro De Giorgi
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