Rocky Mountain Journal of Mathematics 41(5), 1395-1415.
ISSN/ISBN: 0035-7596 DOI: 10.1216/RMJ-2011-41-5-1395
Abstract: This paper is a general treatment of the various notions of densities used in papers on mantissa distribution of sequences of numbers. Equivalence classes of weighted densities are identified, and their hierarchy is stated. This permits us to give clear answers to several questions about the first digit phenomenon. Moreover, however light the weights are, we exhibit an example of a sequence of positive numbers whose mantissae do not admit any distribution in the sense of the corresponding density.
Bibtex:
@article {,
AUTHOR = {Mass{\'e}, Bruno and Schneider, Dominique},
TITLE = {A survey on weighted densities and their connection with the first digit phenomenon},
JOURNAL = {Rocky Mountain J. Math.},
FJOURNAL = {The Rocky Mountain Journal of Mathematics},
VOLUME = {41},
YEAR = {2011},
NUMBER = {5},
PAGES = {1395--1415},
ISSN = {0035-7596},
DOI = {10.1216/RMJ-2011-41-5-1395},
URL = {http://dx.doi.org/10.1216/RMJ-2011-41-5-1395},
}
Reference Type: Journal Article
Subject Area(s): Analysis