Le Veque's superelliptic equation over function fields
R. Mason, B. Brindza (1986)
Acta Arithmetica
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R. Mason, B. Brindza (1986)
Acta Arithmetica
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Serge Lang (1965)
Bulletin de la Société Mathématique de France
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Günter Lettl (2004)
Mathematica Slovaca
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Gunther Cornelissen, Thanases Pheidas, Karim Zahidi (2005)
Journal de Théorie des Nombres de Bordeaux
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We prove that Hilbert’s Tenth Problem for a ring of integers in a number field has a negative answer if satisfies two arithmetical conditions (existence of a so-called set of integers and of an elliptic curve of rank one over ). We relate division-ample sets to arithmetic of abelian varieties.
Michael Nakamaye (1999)
Journal de théorie des nombres de Bordeaux
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We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.
Kae Inoue (2003)
Journal de théorie des nombres de Bordeaux
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We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.
Benoit Arbour, Damien Roy (2004)
Acta Arithmetica
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