A uniform coprimality result for some arithmetic functions |
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Authors: | EJ Scourfield |
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Institution: | Department of Mathematics, Westfield College (University of London), London NW3 7ST, England |
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Abstract: | Using analytic methods, an asymptotic formula, which holds uniformly for squarefree positive integers d in a suitable range, is obtained for the number of positive integers n ≤ x such that (d,f(n)) = 1, where f is an integer-valued multiplicative function such that f(p) is a polynomial in p for p prime, and where d has no prime divisor from a certain finite exceptional set. Examples of such functions f are Euler's function φ and the divisor functions σν (ν = 1,2,…), which case d is assumed to be odd. |
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