2,204 research outputs found
Power-free values of binary forms and the global determinant method
We give an improved estimate for the density of -free values of integral
binary forms with no fixed -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.Comment: 45 pages; final accepted versio
Sextic polynomials in two variables do not represent all non-negative integers
In this paper we prove that for all degree polynomials with rational
coefficients that . The answers a
question of B. Poonen and J. S. Lew in the degree 6 case. This work builds on
previous work with S. Yamagishi.Comment: 11 page
- …