Keith Ramsay, Square-free values of polynomials in one variable over function fields, Internat. Math. Res. Notices (1992), no. 4, 97--102.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with squarefree discriminant: see Section 3. The case of squarefree values of a separable irreducible one variable polynomial over F q [t] or more generally k power free values for polynomials over the ring of regular functions on any a#ne curve over F q ) was proved earlier by K. Ramsay [Ram92] using a lemma of N. Elkies involving a derivation. In Section 8, we sketch a generalization of our result to multivariable polynomials over such rings of regular functions. A related problem asks, given relatively prime polynomials f(x 1 , x n ) and g(x 1 , x n ) over Z, what is ....

..... Let K denote the fraction field of A. For nonzero a A define a : #(A a) and define 0 = 0. If p is a nonzero prime of A, let : #(A p) Define Box = Box(B 1 , B n ) 0 a i if A = Z, a if A = F q [t] The formula for the density in Theorem 1 of [Ram92] should read Z = v##S #(kv) #v# k . The proof there is correct, but the statement is unfortunately misprinted, with #(v) in place of #(kv) For , define B 1 , B n## and define (S) and (S) similarly using lim sup and lim inf in place of lim. If a subset and its 2 ....

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Keith Ramsay, Square-free values of polynomials in one variable over function fields, Internat. Math. Res. Notices (1992), no. 4, 97--102.

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Keith Ramsay, Square-free values of polynomials in one variable over function fields, Internat. Math. Res. Notices (1992), no. 4, 97--102.

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