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On the average number of divisors of quadratic polynomials

Published online by Cambridge University Press:  24 October 2008

James Mckee
James Mckee
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB2 1SB
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Extract

Let d(n) denote the number of positive divisors of n, and let f(x) be a polynomial in x with integer coefficients, irreducible over ℤ. Erdös[3] showed that there exist constants λ1, λ2 (depending on f) such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 3 , May 1995 , pp. 389 - 392
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Bellman, R.. Ramanujan sums and the average value of arithmetic functions. Duke Math. J. 17 (1950), 159–168.CrossRefGoogle Scholar
[2]Davenport, H.. The Higher Arithmetic, 6th edition (Cambridge University Press, 1992).Google Scholar
[3]Erdös, P.. The sum σ d{f(k)}. J. Lond.Math. Soc. 27 (1952), 7–15.CrossRefGoogle Scholar
[4]Hooley, C.. On the representation of a number as the sum of a square and a product. Math. Z. 69 (1958), 211–227.CrossRefGoogle Scholar
[5]Hooley, C.. On the number of divisors of quadratic polynomials. Acta Mathematica 110 (1963), 97–114.CrossRefGoogle Scholar
[6]Hooley, C.. Applications of sieve methods to the theory of numbers. Cambridge Tracts in Mathematics, 70 (Cambridge University Press, 1976).Google Scholar
[7]Scourfield, E. J.. The divisors of a quadratic polynomial. Proc. Glasgow Math. Soc. 5 (1961), 8–20.CrossRefGoogle Scholar