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A generalization of some results in additive number theory

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References

  1. Artin, E., andP. Scherk: On the sum of two sets of integers. Ann. of Math.44, 138–142 (1943).

    Google Scholar 

  2. Brauer, A.: Über die Dichte der Summe zweier Mengen, deren eine von positiver Dichte ist. Math. Z.44, 212–232 (1939).

    Google Scholar 

  3. Corput, J. G. Van Der: On sets of integers I, II, III. Neder. Akad. Wetensch.50, 252–261, 340–350, 429–435 (1947).

    Google Scholar 

  4. Dyson, F. J.: A theorem on the densities of sets of integers. J. London Math. Soc.20, 278–282 (1945).

    Google Scholar 

  5. Erdös, P.: On the arithmetical density of the sum of two sequences one of which forms a basis for integers. Acta Arithmetica1, 197–200 (1936).

    Google Scholar 

  6. —, andI. Niven: The α+β hypothesis and related problems. Amer.Math. Monthly12, 75–78 (1948).

    Google Scholar 

  7. —: Some remarks on number theory. Riveon Lematematika9, 45–48 (1955).

    Google Scholar 

  8. Kasch, F.: Abschätzung der Dichte von Summenmengen. Math. Z.62, 368–387 (1955).

    Google Scholar 

  9. Khintchine, A.: Zur additiven Zahlentheorie. Rec. Math. (Mat. Sbornik)39, 27–34 (1932).

    Google Scholar 

  10. —: Über ein metrisches Problem der additiven Zahlentheorie. Mat. Sbornik40, 180–189 (1933).

    Google Scholar 

  11. Landau, E.: Über einige neuere Fortschritte der additiven Zahlentheorie. Cambridge Tracts No. 35, Cambridge 1937.

  12. Linnik, U. V.: On Erdös's theorem on the addition of numerical sequences. Rec. Math. (Mat. Sbornik), N. S.10, 67–78 (1942).

    Google Scholar 

  13. Mann, H. B.: A proof of the fundamental theorem on the density of sums of sets of positive integers. Ann. of Math.43, 523–529 (1942).

    Google Scholar 

  14. Moser, L.: On the minimal overlap problem of Erdös. Acta Arithmetica5, 117–119 (1959).

    Google Scholar 

  15. Motzkin, T. S., K. E. Ralston andJ. L. Selfridge: Minimal overlap under translation. Abstract Bull. Amer. Math. Soc.62, 558 (1956).

    Google Scholar 

  16. Niven, I.: The asymptotic density of sequences. Bull. Amer. Math. Soc.57, 420–434 (1951).

    Google Scholar 

  17. Ostmann, H. H.: Über die Dichten additiv komponierter Zahlenmengen. Archiv der Mathematik1, 393–401 (1949).

    Google Scholar 

  18. Rohrbach, H.: Einige neueren Untersuchungen über die Dichte in der additiven Zahlentheorie. Jber. Deutsch. Math. Verein.48, 199–236 (1938).

    Google Scholar 

  19. Schnirelmann, L.: Über additive Eigenschaften von Zahlen. Math. Ann.107, 649–690 (1932).

    Google Scholar 

  20. Selberg, S.: Note on a metrical problem in additive theory of numbers. Arch. Math. Naturvidensk.47, 11–118 (1944).

    Google Scholar 

  21. Selberg, S.: A survey of some recent results in additive number theory. Mat. Tidsskr. A, 1–15 (1949).

  22. Stöhr, A.: Bemerkungen zur additiven Zahlentheorie III. Neuer Beweis eines Satzes vonA. Brauer. J. reine angew. Math.195, 172–194 (1955).

    Google Scholar 

  23. Swierczwowski, S.: On the intersection of a linear set with the translation of its complement. Colloquium Mathematicum5, 185–197 (1958).

    Google Scholar 

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Moser, W.O.J. A generalization of some results in additive number theory. Math Z 83, 304–313 (1964). https://doi.org/10.1007/BF01111163

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