seminar: Differential structure of rings and multiplicity problems
speaker: Federico Pellarin (Université Jean Monnet, Saint-Etienne)abstract: Given a linear differential system DY=AY, where A is a m x m matrix with complex rational functions entries, and where Y=(Y1,...,Ym) is a vector of algebraically independent functions, it is known since the seventies that the set of non-zero homogeneous prime ideals P of C(z)Y1,...,Ym such that DP is contained in P has a minimal non-zero element (this was proved by Nesterenko).
However, there does not exist a more general result yet, valid for non-linear differential systems DYj=Pj(Y1,...,Ym) too.
This property is useful to obtain "multiplicity estimates". It is true for the non-linear Ramanujan differential system DY1=(112)(Y12-Y2), DY2=(13)(Y1 Y2-Y3), DY3=(12)(Y1 Y3-Y22), and the correspondent multiplicity estimate, proved by Nesterenko, was used to check the algebraic independence of pi ad epi.
In this talk we discuss about the connection between the property above and multiplicity problems, and we show multiplicity estimates for other non-linear differential systems, which might have diophantine applications.
timetable:
Wed 25 May, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
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