On the representation of numbers by quaternary and quinary cubic forms: I
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.