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Displaying similar documents to “Model theory of fields: An application to positive semidefinite polynomials”

Effective bounds for the zeros of linear recurrences in function fields

Clemens Fuchs, Attila Pethő (2005)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we use the generalisation of Mason’s inequality due to Brownawell and Masser (cf. [8]) to prove effective upper bounds for the zeros of a linear recurring sequence defined over a field of functions in one variable. Moreover, we study similar problems in this context as the equation G n ( x ) = G m ( P ( x ) ) , ( m , n ) ∈ ℕ 2 , where ( G n ( x ) ) is a linear recurring sequence of polynomials and P ( x ) is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].

On the ultrametric Stone-Weierstrass theorem and Mahler's expansion

Paul-Jean Cahen, Jean-Luc Chabert (2002)

Journal de théorie des nombres de Bordeaux

Similarity:

We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If E is a subset of a rank-one valuation domain V , we show that the ring of polynomial functions is dense in the ring of continuous functions from E to V if and only if the topological closure E ^ of E in the completion V ^ of V is compact. We then show how to expand continuous functions in sums of polynomials.