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

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

2003-05-05

arxiv.org/abs/math/0305078v2

Mathematics

Number Theory

version 2, 30 pages. Corrects some typos and statements of propositions 5 and 6 (all theorems and other propositions remain as

Scientific paper

We estimate the number of integer solutions to decomposable form inequalities
(both asymptotic estimates and upper bounds are provided) when the degree of
the form and the number of variables are relatively prime. These estimates
display good behavior in terms of the coefficients of the form, and greatly
improve upon previous estimates in this regard.

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