, Volume 93, Issue 4, pp 329-348

On cubic polynomials

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Abstract

It is shown that a system ofr homogeneous cubic equations with rational coefficients has a nontrivial solution in rational integers if the number of variables is at least (10r)5. For most such systems, an asymptotic formula holds for the numberz P of solutions whose components have modulus <P.

Partially supported by NSF contract NSF-MCS-8015356.