Displaying similar documents to “Approximation exponents for algebraic functions in positive characteristic”

Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

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Thomas’ conjecture is, given monic polynomials p 1 , ... , p d ∈ ℤ [ a ] with 0 < deg p 1 < ⋯ < deg p d , then the Thue equation (over the rational integers) ( X - p 1 ( a ) Y ) ⋯ ( X - p d ( a ) Y ) + Y d = 1 has only trivial solutions, provided a ≥ a 0 with effective computable a 0 . We consider a function field analogue of Thomas’ conjecture in case of degree d = 3 . Moreover we find a counterexample to Thomas’ conjecture for d = 3 .

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici

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We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of ℂ n . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.

Centers in domains with quadratic growth

Agata Smoktunowicz (2005)

Open Mathematics

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Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.