On the number of solutions of decomposable form inequalities

2024/10/01 by Stewart, Cameron L.
#11J87 #FOS: Mathematics #Number Theory (math.NT) #Primary 11D75 #Secondary 11D57

paper · doi:10.48550/arxiv.2410.01097

Abstract

In 2001 Thunder gave an estimate for the number of integer solutions of decomposable form inequalities under the assumption that the forms are of finite type. The purpose of this article is to generalize this result to forms which are of essentially finite type. In the special case of binary forms this gives an improvement of a result of Mahler from 1933.

Related

• Integer solutions of a sequence of decomposable form inequalities
• Asymptotic estimates for the number of integer solutions to decomposable form inequalities
• Decomposable form inequalities
• Finiteness criteria for the solutions of the sequence of semi-decomposable form equations and inequalities
• Bounds for the solutions of S-unit equations and decomposable form equations II