Pacific Journal of Mathematics

A refinement of the fundamental theorem on the density of the sum of two sets of integers.

H. B. Mann

Article information

Source
Pacific J. Math., Volume 10, Number 3 (1960), 909-915.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103038239

Mathematical Reviews number (MathSciNet)
MR0113858

Zentralblatt MATH identifier
0099.26503

Subjects
Primary: 10.00

Citation

Mann, H. B. A refinement of the fundamental theorem on the density of the sum of two sets of integers. Pacific J. Math. 10 (1960), no. 3, 909--915. https://projecteuclid.org/euclid.pjm/1103038239


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References

  • [1] F. J. Dyson, A theorem on the densities of sets of integers, J. London Math. Soc. 2O, (1945), 8-14.
  • [2] A. Y. Khinchin, Three pearls of number theory, Graylock Press, Rochester, New York (1952).
  • [3] H. B. Mann, A proof of the fundamentaltheorem on the density of sums of sets of positive integers, Ann. of Math. 43, (1942), 523-527.
  • [4] Kneser Martin Abschaetzung der asymptotischen Dichte von Summenmengen, Math. Zeitschrift. Bd. 58, (1953), 459-484.
  • [5] J. G. Van der Corput, On sets of integers I II III, Proc. Akad. Wet. Amsterdam 50, (1947), 252-261, 340-350, 429-435.