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

2003/05/05 by Jeffrey Lin Thunder, Thunder, Jeffrey Lin
Mathematics · #11D75 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11D75

paper · pdf · doi:10.48550/arxiv.math/0305078

version 2, 30 pages. Corrects some typos and statements of propositions 5 and 6 (all theorems and other propositions remain as before). The last reference is updated, as well

openalex publication_date 2003/05/05 · arxiv created 2003/11/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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