Abstract
Denote by \(s_0^{(r)}\) the least integer such that if \(s \geqslant s_0^{(r)}\), and \(F\) is a cubic form with real coefficients in \(s\) variables that splits into \(r\) parts, then \(F\) takes arbitrarily small values at nonzero integral points. We bound \(s_0^{(r)}\) for \(r \leqslant 6\).
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Communicated by J. Schoißengeier.
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Chow, S. Cubic diophantine inequalities for split forms. Monatsh Math 175, 213–225 (2014). https://doi.org/10.1007/s00605-013-0604-0
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DOI: https://doi.org/10.1007/s00605-013-0604-0