Representation of Small Integers by Binary Forms

2015/08/14 by Akhtari, Shabnam
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1508.03602

Abstract

We establish some upper bounds for the number of integer solutions to the Thue inequality |F(x , y)| ≤ m, where F is a binary form of degree n ≥ 3 and with non-zero discriminant D, and m is an integer. Our upper bounds are independent of m, when m is smaller than |D|^(1)/(4(n-1)). We also consider the Thue equation |F(x , y)| = m and give some upper bounds for the number of its integral solutions. In the case of equation, our upper bounds will be independent of integer m, when m < |D|^(1)/(2(n-1)).

Related

• Cubic Thue inequalities with positive discriminant
• Representation of Unity by Binary Forms
• Explicit and Mixed Estimates for Thue inequalities with few coefficients
• Cubic Thue Equations
• Diagonalizable Thue Equations -- revisited