Limit theorems for divisor distributions
HTML articles powered by AMS MathViewer
- by Michael D. Vose PDF
- Proc. Amer. Math. Soc. 95 (1985), 505-511 Request permission
Abstract:
For a positive integer $N$, let ${X_N}$ be a random variable uniformly distributed over the set $\{ \log d:d|N\}$. Let ${F_N}$ be the normalized (to have expectation zero and variance one) distribution function for ${X_N}$. Necessary and sufficient conditions for the convergence of a sequence ${F_{{N_j}}}$ of distributions are given. The possible limit distributions are investigated, and the case where the limit distribution is normal is considered in detail.References
- John B. Conway, Functions of one complex variable, 2nd ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1978. MR 503901
- Paul Erdős and Jean-Louis Nicolas, Méthodes probabilistes et combinatoires en théorie des nombres, Bull. Sci. Math. (2) 100 (1976), no. 4, 301–320 (French). MR 506129
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- D. S. Mitrinović, Analytic inequalities, Die Grundlehren der mathematischen Wissenschaften, Band 165, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. MR 0274686
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 505-511
- MSC: Primary 11N60; Secondary 11K65
- DOI: https://doi.org/10.1090/S0002-9939-1985-0810153-0
- MathSciNet review: 810153