Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Probability methods in some problems of analysis and number theory
HTML articles powered by AMS MathViewer

by M. Kac PDF
Bull. Amer. Math. Soc. 55 (1949), 641-665
References
    S. Banach 1. Ueber einige Eigenschaften der lakunären trigonometrischen Reihen, Studia Mathematica vol. 2 (1930) pp. 207-220. H. Davenport 1. Ueber Numeri Abundantes, Preuss. Akad. Wiss. Sitzungsber. (1930) pp. 830-837.
  • P. Erdös, On the strong law of large numbers, Trans. Amer. Math. Soc. 67 (1949), 51–56. MR 32971, DOI 10.1090/S0002-9947-1949-0032971-4
  • P. Erdös 2. Note on the number of prime divisors of integers, J. London Math. Soc. vol. 12 (1937) pp. 308-314.
  • P. Erdös, On the distribution function of additive functions, Ann. of Math. (2) 47 (1946), 1–20. MR 15424, DOI 10.2307/1969031
  • P. Erdös 4. On a problem of Chowla and some related problems, Proc. Cambridge Philos. Soc. vol. 32 (1936) pp. 530-540. P. Erdös 5. On the density of some sequences of numbersI, J. London Math. Soc. vol. 10 (1935) pp. 120-125. P. Erdös 6. On the density of some sequences of numbersII, ibid. vol. 12 (1937) pp. 7-11. P. Erdös 7. On the density of some sequences of numbersIII, ibid. vol. 13 (1938) pp. 119-127.
  • 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. MR 2374, DOI 10.2307/2371483
  • Paul Erdös and Aurel Wintner, Additive arithmetical functions and statistical independence, Amer. J. Math. 61 (1939), 713–721. MR 247, DOI 10.2307/2371326
  • W. Feller, The fundamental limit theorems in probability, Bull. Amer. Math. Soc. 51 (1945), 800–832. MR 13252, DOI 10.1090/S0002-9904-1945-08448-1
  • Jacqueline Ferrand and Robert Fortet, Sur des suites arithmétiques équiréparties, C. R. Acad. Sci. Paris 224 (1947), 516–518 (French). MR 19258
  • R. Fortet, Sur une suite egalement répartie, Studia Math. 9 (1940), 54–70 (French, with Ukrainian summary). MR 5546, DOI 10.4064/sm-9-1-54-70
  • G. H. Hardy and S. Ramanujan 1. The normal number of prime factors of a number n, Quart. J. Math. Oxford Ser. vol. 48 (1917) pp. 76-92.
  • Philip Hartman, The divergence of non-harmonic gap series, Duke Math. J. 9 (1942), 404–405. MR 6768
  • Shin-ichi Izumi and Tatsuo Kawata, On certain series of functions, Tôhoku Math. J. 46 (1939), 91–105. MR 1322
  • M. Kac, Note on Power Series with Big Gaps, Amer. J. Math. 61 (1939), no. 2, 473–476. MR 1507389, DOI 10.2307/2371514
  • M. Kac 2. Distribution properties of certain gap sequences, Bull. Amer. Math. Soc. Abstract 53-7-290. Details will be given in the paper by Erdös, Ferrand, Fortet and Kac (see footnote 2). The following misprint should be corrected: ω/2cos πk| should be replaced by ω/2|cos πx|.
  • M. Kac, On the distribution of values of sums of the type $\sum f(2^k t)$, Ann. of Math. (2) 47 (1946), 33–49. MR 15548, DOI 10.2307/1969033
  • M. Kac, Convergence of certain gap series, Ann. of Math. (2) 44 (1943), 411–415. MR 8432, DOI 10.2307/1968972
  • M. Kac, Convergence and divergence of non-harmonic gap series, Duke Math. J. 8 (1941), 541–545. MR 5143
  • M. Kac 6. Sur les fonctions indépendantesV, Studia Mathematica vol. 7 (1938) pp. 96-100.
  • M. Kac, Note on the distribution of values of the arithmetic function $d(m)$, Bull. Amer. Math. Soc. 47 (1941), 815–817. MR 4845, DOI 10.1090/S0002-9904-1941-07575-0
  • M. Kac, R. Salem, and A. Zygmund, A gap theorem, Trans. Amer. Math. Soc. 63 (1948), 235–243. MR 23937, DOI 10.1090/S0002-9947-1948-0023937-8
  • S. Kaczmarz and H. Steinhaus 1. Le système orthogonal de M. Rademacher, Studia Mathematica vol. 2 (1930) pp. 231-247. A. Khintchine and A. Kolmogoroff 1. Ueber Konvergenz von Reihen deren Glieder durch den Zufall bestimmt werden, Rec. Math. (Mat. Sbornik) vol. 32 (1925) pp. 668-677.
  • A. Kolmogoroff, Über die Summen durch den Zufall bestimmter unabhängiger Größen, Math. Ann. 99 (1928), no. 1, 309–319 (German). MR 1512451, DOI 10.1007/BF01459098
  • A. Kolmogoroff 2. Bemerkungen zu meiner Arbeit "Ueber die summen Zufälliger Grössen", ibid. vol. 102 (1929) pp. 484-489. A. Kolmogoroff 3. Une contribution à l’étude de la convergence des séries de Fourier, Fund. Math. vol. 5 (1924) pp. 96-97. P. Lévy 1. Sur les séries dont les termes sont des variables éventuelles indépendantes, Studia Mathematica vol. 3 (1931) pp. 119-155. W. J. LeVeque 1. On the distribution of values of number-theoretic functions, Thesis, Cornell University. R. E. A. C. Paley and A. Zygmund 1. On some series of functions (1), Proc. Cambridge Philos. Soc. vol. 26 (1930) pp. 337-357. R. E. A. C. Paley and A. Zygmund 2. On some series of functions (2), ibid. pp. 458-474. R. E. A. C. Paley and A. Zygmund 3. On some series of functions (3), ibid. vol. 28 (1932) pp. 190-205.
  • Hans Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), no. 1-2, 112–138 (German). MR 1512104, DOI 10.1007/BF01458040
  • D. Raikov 1. On some arithmetical properties of summable functions, Rec. Math. (Mat. Sbornik) N.S. vol. 1 (1936) pp. 377-383.
  • Frédéric Riesz, Sur la théorie ergodique, Comment. Math. Helv. 17 (1945), 221–239 (French). MR 14218, DOI 10.1007/BF02566244
  • R. Salem and A. Zygmund, On lacunary trigonometric series, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 333–338. MR 22263, DOI 10.1073/pnas.33.11.333
  • R. Salem and A. Zygmund, On lacunary trigonometric series. II, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 54–62. MR 23936, DOI 10.1073/pnas.34.2.54
  • I. J. Schoenberg 1. Ueber die asymptötische Verteilung reeller Zahlenmod 1, Math. Zeit. vol. 28 (1928) pp. 171-200.
  • I. J. Schoenberg, On asymptotic distributions of arithmetical functions, Trans. Amer. Math. Soc. 39 (1936), no. 2, 315–330. MR 1501849, DOI 10.1090/S0002-9947-1936-1501849-X
  • H. Steinhaus 1. Les probabilités dénombrables et leur rapport à la théorie de la mesure, Fund. Math. vol. 4 (1922) pp. 286-310. P. Turán 1. Ueber einige Verallgemeinerungen eines Satzes von Hardy und Ramanujan, J. London Math. Soc. vol. 11 (1936) pp. 125-133. A. Zygmund 1. On the convergence of lacunary trigonometric series, Fund. Math. vol. 16 (1930) pp. 90-107.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 55 (1949), 641-665
  • DOI: https://doi.org/10.1090/S0002-9904-1949-09242-X
  • MathSciNet review: 0031504