Solutions to infinite families of complex cubic Thue equations.
Emery Thomas (1993)
Journal für die reine und angewandte Mathematik
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Emery Thomas (1993)
Journal für die reine und angewandte Mathematik
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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...
R. Conti (1990)
Annales Polonici Mathematici
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Livio Zefiro, Maria Rosa Ardigo (2009)
Visual Mathematics
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Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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C. Hooley (2016)
Acta Arithmetica
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On the assumption of a Riemann hypothesis for certain Hasse-Weil L-functions, it is shewn that a quaternary cubic form f(x) with rational integral coefficients and non-vanishing discriminant represents through integral vectors x almost all integers N having the (necessary) property that the equation f(x)=N is soluble in every p-adic field ℚₚ. The corresponding proposition for quinary forms is established unconditionally.
Yasutsugu Fujita, Tadahisa Nara (2015)
Acta Arithmetica
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We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell-Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.
G. Greaves (1970)
Acta Arithmetica
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P. Pleasants (1966)
Acta Arithmetica
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Andrew Bremner (1989)
Manuscripta mathematica
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Sheldon Katz (1987)
Mathematische Zeitschrift
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J.-H. Evertse (1983)
Inventiones mathematicae
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J.H. Evertse (1984)
Inventiones mathematicae
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Milnor, John (1992)
Experimental Mathematics
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