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1 results

  • Asymptotic estimates for the number of integer solutions to decomposable form inequalities

  • Jeffrey Lin Thunder
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 2 / March 2005
    Published online by Cambridge University Press:
    10 February 2005, pp. 271-292
    Print publication:
    March 2005
    • Article
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  • For homogeneous decomposable forms F(X) in n variables with integer coefficients, we consider the number of integer solutions ${\bf x}\in\mathbb{Z}^n$ to the inequality $|F({\bf x})|\le m$ as $m\rightarrow\infty$. We give asymptotic estimates which improve on those given previously by the author in Ann. of Math. (2) 153 (2001), 767–804. Here our error terms display desirable behaviour as a function of the height whenever the degree of the form and the number of variables are relatively prime.