Displaying similar documents to “How Many Algebraic (Finite) Extensions Over The Rationals”

On ruled fields

Jack Ohm (1989)

Journal de théorie des nombres de Bordeaux

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Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.

Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II

Peter Bundschuh, Keijo Väänänen (2015)

Acta Arithmetica

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This article continues a previous paper by the authors. Here and there, the two power series F(z) and G(z), first introduced by Dilcher and Stolarsky and related to the so-called Stern polynomials, are studied analytically and arithmetically. More precisely, it is shown that the function field ℂ(z)(F(z),F(z⁴),G(z),G(z⁴)) has transcendence degree 3 over ℂ(z). This main result contains the algebraic independence over ℂ(z) of G(z) and G(z⁴), as well as that of F(z) and F(z⁴). The first...