We investigate the density of square-free values of polynomials with large coefficients over the rational function field 𝔽q[t]. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial N as a sum of a k-th power of a small polynomial and a square-free polynomial.

中文翻译：

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关于有理函数域上大多项式的无平方值

我们研究了有理函数场上具有大系数的多项式的无平方值的密度𝔽q[吨]。作为我们结果的特殊情况，我们回答了一些有趣的问题，包括短间隔内无平方多项式的密度，以及大型多项式的表示数量的渐近ñ作为一个总和ķ小多项式和无平方多项式的 -th 次方。