Note on autopolar plane cubics
Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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Hari das Bagchi, Manindra Chandra Chaki (1952)
Rendiconti del Seminario Matematico della Università di Padova
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J. Coates (1970)
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...
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, Maria Rosa Ardigo (2009)
Visual Mathematics
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Isao Wakabayashi (2003)
Acta Arithmetica
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R. Conti (1990)
Annales Polonici Mathematici
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Jean-Marc Deshouillers (1990)
Journal de théorie des nombres de Bordeaux
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Haridas Bagchi, Biswarup Mukherji (1951)
Rendiconti del Seminario Matematico della Università di Padova
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Milnor, John (1992)
Experimental Mathematics
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S Chowla, H Davenport (1961)
Acta Arithmetica
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