Monatshefte für Mathematik

, Volume 93, Issue 4, pp 329–348

On cubic polynomials

IV. systems of rational equations
  • Wolfgang M. Schmidt

DOI: 10.1007/BF01295233

Cite this article as:
Schmidt, W.M. Monatshefte für Mathematik (1982) 93: 329. doi:10.1007/BF01295233


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 numberzPof solutions whose components have modulus <P.

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Wolfgang M. Schmidt
    • 1
  1. 1.Mathematics DepartmentUniversity of ColoradoBoulderUSA