Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the size of certain number-theoretic functions

Author: Wm. J. LeVeque
Journal: Trans. Amer. Math. Soc. 66 (1949), 440-463
MSC: Primary 10.0X
MathSciNet review: 0030993
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] A. C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Amer. Math. Soc. vol. 49 (1941) pp. 122-136. MR 0003498 (2:228i)
  • [2] V. Brun, Le crible d'Eratosthene et la théorème de Goldbach, Skrifter Videns, Kristiana, 1920.
  • [3] H. Cramér, Mathematical methods of statistics, Princeton University Press, 1946. MR 0016588 (8:39f)
  • [4] P. Erdös, On a problem of Chowla and some related problems, Proc. Cambridge Philos. Soc. vol. 32 (1936) pp. 530-540.
  • [5] -, Note on the number of prime divisors of integers, J. London Math. Soc. vol. 12 (1937) pp. 308-314.
  • [6] -, On the distribution function of additive functions, Ann. of Math. vol. 47 (1946) pp. 1-20. MR 0015424 (7:416c)
  • [7] P. Erdös and M. Kac, The Gaussian law of errors in the theory of additive number-theoretic functions, Amer. J. Math. vol. 62 (1940) pp. 738-742. MR 0002374 (2:42c)
  • [8] P. Erdös and A. Wintner, Additive arithmetical functions and statistical independence, Amer. J. Math. vol. 61 (1939) pp. 713-721. MR 0000247 (1:40c)
  • [9] G. H. Hardy and E. M. Wright, The theory of numbers, Oxford Press, 1938.
  • [10] P. L. Hsu, The approximate distributions of the mean and variance of a sample of independent variables, Ann. Math. Statist, vol. 16 (1945) pp. 1-29. MR 0011911 (6:233b)
  • [11] M. Kac, Note on the distribution of values of the arithmetic function $ d(m)$, Bull. Amer. Math. Soc. vol. 47 (1941) pp. 815-817. MR 0004845 (3:69e)
  • [12] -, Note on partial sums of the exponential series, Revista de la Universidad Nacional de Tucumán, Serie A, Matematicas y Fisica Teorica, vol. 3 (1942) pp. 151-153. MR 0007799 (4:194g)
  • [13] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Teubner, 1909.
  • [14] J. B. Rosser and W. J. Harrington, Brun's method in number theory, to be published soon.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10.0X

Retrieve articles in all journals with MSC: 10.0X

Additional Information

Article copyright: © Copyright 1949 American Mathematical Society

American Mathematical Society