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arXiv · 1505.05587

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

Stanley Yao Xiao
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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.

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Stanley Yao Xiao. 2017-12-22. Power-free values of binary forms and the global determinant method. https://doi.org/10.1093/imrn%2Frnw165

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