Positive values of inhomogeneous quadratic forms of signature -2
Continuing work of \textit{H. Blaney} [J. Lond. Math. Soc. 23, 153-160 (1948; Zbl 0031.20404)] and \textit{R. P. Bambah}, \textit{V. C. Dumir} and \textit{R. J. Hans-Gill} [Colloq. Math. Soc. Janos Bolyai 34, 111-170 (1984; Zbl 0537.10019) and J. Number Theory 16, 403-419 (1983; Zbl 0514.10024)] the authors investigate small positive values of a real indefinite inhomogeneous quadratic form \(Q(x_ 1+r_ 1,...,x_ n+r_ n)\) of signature -2 in integral variables \(x_ i\). They find that any such form of discriminant 1 in \(n\geq 10\) variables assumes values \(\leq 2\cdot 3^{-1/n}\) and that this bound is best possible (this happens to be the same bound as for forms of signature \(+2)\).
scientific article; zbMATH DE number 4053732
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