Acta Mathematica

, Volume 110, Issue 1, pp 97–114 | Cite as

On the number of divisors of quadratic polynomials

  • Christopher Hooley
Article

Keywords

Quadratic Polynomial 

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References

  1. [1].
    Bellman, R., Ramanujan sums and the average value of arithmetical functions.Duke Math. J., 17 (1950), 159–168.MATHMathSciNetCrossRefGoogle Scholar
  2. [2].
    Erdös, P., On the sum Σd{f(k)}.J. London Math. Soc., 27 (1952), 7–15.MATHMathSciNetGoogle Scholar
  3. [3].
    Gauss, K. F.,Disquisitiones arithmeticae, 1801.Google Scholar
  4. [4].
    Hardy, G. H.,Divergent series. Oxford Univ. Press, 1948.Google Scholar
  5. [5].
    Hooley, C., On the representation of a number as the sum of a square and a product.Math. Z. 69 (1958), 211–227.MATHMathSciNetCrossRefGoogle Scholar
  6. [6].
    —, An asymptotic formula in the theory of numbers.Proc. London Math. Soc., Ser. 3, 7 (1957), 396–413.MATHMathSciNetGoogle Scholar
  7. [7].
    Ingham, A. E., Some asymptotic formulae in the theory of numbersJ. London Math. Soc., 2 (1927), 202–208.MATHGoogle Scholar
  8. [8].
    Scourfield, E. J., The divisors of a quadratic polynomial.Proc. Glasgow Math. Soc., 5 (1961), 8–20.MATHMathSciNetCrossRefGoogle Scholar
  9. [9].
    Smith, H. J. S.,Collected Mathematical Papers, Vol. 1, 1894.Google Scholar

Copyright information

© Almqvist & Wiksells Boktryckeri AB 1963

Authors and Affiliations

  • Christopher Hooley
    • 1
  1. 1.Bristol UniversityEngland

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