On quasi-periods of abelian functions with complex multiplication
D. W. Masser (1980)
Mémoires de la Société Mathématique de France
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Displaying similar documents to “The transcendence of certain quasi-periods associated with abelian functions in two variables”
On quasi-periods of abelian functions with complex multiplication
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Small values of the quadratic part of the Néron-Tate height on an abelian variety
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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...
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We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.