On a family of cubic Thue equations with 5 solutions
Isao Wakabayashi (2003)
Acta Arithmetica
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Isao Wakabayashi (2003)
Acta Arithmetica
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Jun Ho Lee, Stéphane R. Louboutin (2014)
Acta Arithmetica
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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...
Andrew Bremner (1989)
Manuscripta mathematica
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Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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R. Conti (1990)
Annales Polonici Mathematici
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Sahib Ram Mandan (1981)
Časopis pro pěstování matematiky
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Dragan M. Acketa, Joviša Žunić (1996)
Publications de l'Institut Mathématique
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Haridas Bagchi, Biswarup Mukherji (1951)
Rendiconti del Seminario Matematico della Università di Padova
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Duquesne, Sylvain (2001)
Experimental Mathematics
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Emery Thomas (1993)
Journal für die reine und angewandte Mathematik
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Bjorn Poonen (2001)
Journal de théorie des nombres de Bordeaux
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We prove that for any , the curve in is a genus curve violating the Hasse principle. An explicit Weierstrass model for its jacobian is given. The Shafarevich-Tate group of each contains a subgroup isomorphic to .
Tim Dokchitser (2007)
Acta Arithmetica
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