On square-free values of large polynomials over the rational function field
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Abstract We investigate the density of square-free values of polynomials with large coefficients over the rational function field 𝔽 q [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.
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2006 ◽
Vol 74
(3)
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pp. 461-470
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2003 ◽
Vol 113
(2)
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pp. 153-163
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1993 ◽
Vol 48
(2)
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pp. 313-319
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2015 ◽
Vol 373
(2040)
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pp. 20140311
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