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Waring's problem for sets of density zero

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Analytic Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 899))

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References

  1. P. T. Bateman, On the representations of a number as the sum of three squares, Trans. Amer. Math. Soc. 71 (1951), 70–101.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. L. G. Choi, P. Erdös, and M. B. Nathanson, Lagrange's theorem with N1/3 squares, Proc. Amer. Math. Soc. 79 (1980), 203–205.

    MathSciNet  MATH  Google Scholar 

  3. P. Erdös and M. B. Nathanson, Lagrange's theorem and thin subsequences of squares, in J. Gani and V. K. Rohatgi, editors, Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs, Academic Press, New York, 1981.

    Google Scholar 

  4. P. Erdös and A. Rényi, Additive properties of random sequences of positive integers, Acta. Arithm. 6 (1960), 83–110.

    MathSciNet  MATH  Google Scholar 

  5. H. Halberstam and K. F. Roth, Sequences Vol. I, Clarendon Press, Oxford, 1966.

    MATH  Google Scholar 

  6. G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio Numerorum': IV. The singular series in Waring's Problem and the value of the number G(k), Math. Zeit, 12 (1922), 161–188.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Hilbert, Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsche Problem), Math. Ann. 67 (1909), 281–300.

    Article  MathSciNet  MATH  Google Scholar 

  8. L. G. Shnirel'man, On additive properties of integers, Izvestiyakh Donskogo Instituta v Novocherkasske 14 (1930), 3–27.

    Google Scholar 

  9. C. L. Siegel, Über die Klassenzahl quadratische Zahlkörper, Acta Arith. 1 (1935), 83–86.

    Google Scholar 

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Marvin I. Knopp

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Dedicated to Emil Grosswald

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© 1981 Springer-Verlag

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Nathanson, M.B. (1981). Waring's problem for sets of density zero. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096469

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  • DOI: https://doi.org/10.1007/BFb0096469

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  • Print ISBN: 978-3-540-11173-3

  • Online ISBN: 978-3-540-38953-8

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