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- W2559945514 abstract "Let $F$ be a binary form with integer coefficients, non-zero discriminant and degree $d$ with $d$ at least $3$ and let $r$ denote the largest degree of an irreducible factor of $F$ over the rationals. Let $k$ be an integer with $k geq 2$ and suppose that there is no prime $p$ such that $p^k$ divides $F(a,b)$ for all pairs of integers $(a,b)$. Let $R_{F,k}(Z)$ denote the number of $k$-free integers of absolute value at most $Z$ which are represented by $F$. We prove that there is a positive number $C_{F,k}$ such that $R_{F,k}(Z)$ is asymptotic to $C_{F,k} Z^{frac{2}{d}}$ provided that $k$ exceeds $ frac{7r}{18}$ or $(k,r)$ is $(2,6)$ or $(3,8)$." @default.
- W2559945514 created "2016-12-16" @default.
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- W2559945514 date "2020-08-20" @default.
- W2559945514 modified "2023-10-16" @default.
- W2559945514 title "On the representation of $k$-free integers by binary forms" @default.
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- W2559945514 doi "https://doi.org/10.4171/rmi/1213" @default.
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