Monatshefte für Mathematik

, Volume 93, Issue 4, pp 329-348

First online:

On cubic polynomials

IV. systems of rational equations
  • Wolfgang M. SchmidtAffiliated withMathematics Department, University of Colorado

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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.