Cubic diophantine inequalities for split forms

Abstract

Denote by $s_0^{(r)}$ the least integer such that if $s\ge s_0^{(r)}$, 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 $r\le 6$.

References in corpus (1)

• Rational points on cubic hypersurfaces that split off two forms