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On square-free values of large polynomials over the rational function field
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.6 ) Pub Date : 2019-12-12 , DOI: 10.1017/s0305004119000392 DAN CARMON , ALEXEI ENTIN
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.6 ) Pub Date : 2019-12-12 , DOI: 10.1017/s0305004119000392 DAN CARMON , ALEXEI ENTIN
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:
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。
更新日期:2019-12-12
中文翻译:
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𝔽