Acta Mathematica Hungarica

, Volume 53, Issue 3–4, pp 347–365 | Cite as

The exceptional set for the sum of a prime and a square

  • R. Brünner
  • A. Perelli
  • J. Pintz


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E. Bombieri, Le Grand Crible dans la Théorie Analytique des Nombres,Astérisque,18 (1974).Google Scholar
  2. [2]
    H. Davenport,Multiplicative Number Theory, 2nd edition, Springer-Verlag, 1980.Google Scholar
  3. [3]
    H. Davenport, H. Heilbronn, Note on a result in the additive theory of numbers,Proc. London Math. Soc.,43 (1937), 142–151.Google Scholar
  4. [4]
    H. Davenport, H. Heilbronn, On indefinite quadratic forms in five variables,J. London Math. Soc.,21 (1946), 185–193.Google Scholar
  5. [5]
    P. X. Gallagher, A large sieve density estimate near δ=1,Inventiones Math.,11 (1970), 329–339.CrossRefGoogle Scholar
  6. [6]
    G. H. Hardy, J. E. Littlewood, Some problems of partitio numerorum III: on the expression of a large number as a sum of primes,Acta Math.,44 (1923), 1–70.Google Scholar
  7. [7]
    R. J. Miech, On the equationn=p+x 2,Trans. Amer. Math. Soc.,130 (1986), 494–512.Google Scholar
  8. [8]
    R. J. Miech, A number theoretic constant,Acta Arith.,15 (1969), 119–137.Google Scholar
  9. [9]
    H. L. Montgomery,Topics in Multiplicative Number Theory, Springer Lecture Notes n0 227, 1971.Google Scholar
  10. [10]
    H. L. Montgomery, R. C. Vaughan, The exceptional set in Goldbach's problem,Acta Arith.,27 (1975), 353–370.Google Scholar
  11. [11]
    I. V. Polyakov, On the exceptional set of a sum of a prime and a perfect square, translate in:Soviet Math. Doklady,24 (1981), 464–466.Google Scholar
  12. [12]
    I. V. Polyakov, On the exceptional set for the sum of a prime and a perfect square, translated in:Math. U.S.S.R. Izvestija,19 (1982), 611–641.Google Scholar
  13. [13]
    E. C. Titchmarsh,The theory of the Riemann Zeta-Function, Oxford U.P., 1951.Google Scholar
  14. [14]
    R. C. Vaughan, On Goldbach's problem,Acta Arith.,22 (1972), 21–48.Google Scholar
  15. [15]
    A. I. Vinogradov, On a binary problem of Hardy-Littlewood (Russian),Acta Arith.,46 33–56.Google Scholar

Copyright information

© Akadémia Kiadó 1989

Authors and Affiliations

  • R. Brünner
    • 1
  • A. Perelli
    • 2
  • J. Pintz
    • 3
  1. 1.Neufahrn
  2. 2.Dipartimento di MatematicaUniversita di GenovaGenovaItaly
  3. 3.Mathematical Institute of the Hungarian Academy of SciencesBudapest

Personalised recommendations