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Moments of additive functions and sieve methods

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Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1052))

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References

  1. K. Alladi, A study of the moments of additive functions using Laplace transforms and sieve methods, to appear.

    Google Scholar 

  2. H. Delange, Sur le nombre des diviseurs premiers de n, C.R. Acad. Sci. Paris, 237 (1953), 542–544.

    MathSciNet  MATH  Google Scholar 

  3. H. Delange, Sur un théorème d'Erdös et Kac, Acad. Roy. Belg. Bull. Cl. Sci., 5, 42(1956), 130–144.

    MathSciNet  MATH  Google Scholar 

  4. H. Delange, Sue les fonctions arithmetiques fortement additives, C.R. Acad. Sci. Paris, 244(1957), 2122–2124.

    MathSciNet  MATH  Google Scholar 

  5. P.D.T.A. Elliott, Probabilistic Number Theory, Vol. 1 and 2, Grundelehren 239–240, Springer-Verlag, Berlin, New York (1980).

    Book  Google Scholar 

  6. P.D.T.A. Elliott, High power analogues of the Turán-Kubilius inequality and an application to number theory, Can. J. Math., 32(1980), 893–907.

    Article  MATH  Google Scholar 

  7. P. Erdös, On the density of some sequences of numbers I,II,III, J. London Math. Soc., 10(1935), 120–125; 12(1937), 7–11; 13(1938), 119–127.

    Article  MATH  Google Scholar 

  8. P. Erdös and M. Kac, The Gaussian law of errors in the theory of additive number theoretic functions, Amer. J. Math., 62(1940), 738–742.

    Article  MathSciNet  MATH  Google Scholar 

  9. P. Erdös and A. Wintner, Additive arithmetic functions and statistical independence, Amer. J. Math., 61(1939), 713–721.

    Article  MathSciNet  MATH  Google Scholar 

  10. R.R. Hall, Halving an estimate obtained from Selberg's upper bound method, Acta. Arith., 25(1974), 347–351.

    MATH  Google Scholar 

  11. H. Halberstam, On the distribution of additive number theoretic functions. I, II, III, J. London Math. Soc., 30(1956), 43–53; 31(1956), 1–14; 31(1956), 14–27.

    MathSciNet  MATH  Google Scholar 

  12. H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London-New York (1974).

    MATH  Google Scholar 

  13. G.H. Hardy and S. Ramanujan, On the normal number of prime factors of a number n, Quart, J. Math., Oxford, 48(1917), 76–92.

    MATH  Google Scholar 

  14. M. Kac, Probability methods in some problems of analysis and number theory, Bull. Amer. Soc., 55(1949), 641–665.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Kubilius, Probabilistic methods in the theory of numbers, Uspekhi Math. Nauk., N.S. 11(1956), 2(68), 31–66 = Amer. Math. Soc. Translations 19(1962), 47–85.

    MathSciNet  MATH  Google Scholar 

  16. J. Kubilius, Probabilistic methods in the theory of numbers, Amer. Math. Soc. Translations of Mathematical Monographs, 11, Providence (1964).

    Google Scholar 

  17. H.L. Montgomery, Topics in multiplicative number theory, Springer-Lecture Notes No. 227, Berlin (1971).

    Google Scholar 

  18. A. Rényi and P. Turán, On a theorem of Erdös-Kac, Acta. Arith., 4(1958), 71–84.

    MathSciNet  MATH  Google Scholar 

  19. P. Turán, On a theorem of Hardy and Ramanujan, J. London Math. Soc., 9(1934), 274–276.

    Article  MathSciNet  MATH  Google Scholar 

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David V. Chudnovsky Gregory V. Chudnovsky Harvey Cohn Melvin B. Nathanson

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© 1984 Springer-Verlag

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Alladi, K. (1984). Moments of additive functions and sieve methods. In: Chudnovsky, D.V., Chudnovsky, G.V., Cohn, H., Nathanson, M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071538

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  • DOI: https://doi.org/10.1007/BFb0071538

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12909-7

  • Online ISBN: 978-3-540-38788-6

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