Platonic and Catalan Polyhedra as Archetypes of Forms Belonging to the Cubic and Icosahedral Systems
Livio Zefiro, Maria Rosa Ardigo (2009)
Visual Mathematics
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Livio Zefiro, Maria Rosa Ardigo (2009)
Visual Mathematics
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J.-H. Evertse (1983)
Inventiones mathematicae
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J.H. Evertse (1984)
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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.
Livio Zefiro (2010)
Visual Mathematics
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G. Greaves (1970)
Acta Arithmetica
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Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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Christopher Hooley (1991)
Journal für die reine und angewandte Mathematik
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R.W. Bruggeman (1978)
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Proskurin, N.V. (2004)
Zapiski Nauchnykh Seminarov POMI
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Jun Ho Lee, Stéphane R. Louboutin (2014)
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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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