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- W2167537257 abstract "In 1935 Tartakowski (7) proved that, in general, a cubic form in sufficiently many variables with coefficients in an algebraic number field K has a non-trivial zero in that field; and in the case when K is the rational field 57 variables suffice. Here, ‘in general’ means that the coefficients of the form do not lie in a proper subvariety of the coefficient space. Hence, Tartakowski's result holds for almost all cubic forms. Later, Lewis (5) proved that if K is any algebraic number field such that [ K : Q ] = n, then there exists a function ψ( n ) such that every cubic form over K in m ≥ ψ( n ) variables has a non-trivial zero in K . His bound, ψ( n ), is extremely large; e.g. when K is the rational field, ψ(1) > 500." @default.
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- W2167537257 date "1969-09-01" @default.
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- W2167537257 title "Cubic forms over algebraic number fields" @default.
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- W2167537257 doi "https://doi.org/10.1017/s0305004100045011" @default.
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