Stanley Yao Xiao

Power-Free Values of Binary Forms and the Global Determinant Method

We give an improved estimate for the density of

On the representation of integers by binary forms

k

Zeroes of polynomials in many variables with prime inputs

-free values of integral binary forms with no fixed

Zeroes of polynomials with prime inputs and Schmidt's

k

h

-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.