Mixing Sequences of Random Variables and Probabilistic Number Theory

Download or read book Mixing Sequences of Random Variables and Probabilistic Number Theory written by Walter Philipp and published by American Mathematical Soc.. This book was released on 1971 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author gives a solution to the central limit problem and proves several forms of the iterated logarithm theorem and the results are then applied to the following branches of number theory: limit theorems for continued fractions and related algorithms; limit theorems in Diophantine approximations; discrepancies of sequences uniformly distributed mod one and the distribution of additive functions. In addition to new results, the major contribution of the work is the unification of the listed branches of probabilistic number theory. In particular, this is the first time that the distribution theory of additive functions has been related to metric number theory.