Power-free values of binary forms and the global determinant method

Abstract

We give an improved estimate for the density of $k$-free values of integral binary forms with no fixed $k$-th power divisor. Further, we give the corresponding improvement to a theorem of Stewart and Top on the number of power-free values in an interval that may be assumed by a binary form. The approach we use involves a generalization of the global determinant method of Salberger.

45 pages; final accepted version

References in corpus (2)

• The density of rational points in curves and surfaces
• Powerfree Values of Polynomials

Cited by in corpus (3)

• Density of power-free values of polynomials
• On the representation of $k$-free integers by binary forms
• Elliptic curves with a rational 2-torsion point ordered by conductor and the boundedness of average rank