Elem. Math. 60, pp. 10-18.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Note - this is a foreign language paper: FRE
Abstract: When one considers numerical data taken from various sources such as Stock Exchange values, areas of African lakes, weights of chemical compounds ..., one observes that the nine digits 1,2,...,9 do not occur as the first digit (the one on the left) in these numbers with uniform probability: in the 1930’s, F. Benford gathered more than 20 000 such numerical samples and observed that each digit d occurs with probability approximately log(1+1/d). One can wonder if such a law still holds for sequences (a_{n})_{n≥0} contained in [1,+∞[ such as the Fibonacci sequence, or, more generally, for sequences defined by linear recurrence relations. For instance, the sequence a_{n} = 2^{n} satisfies Benford’s Law, as is shown in [1] as an application of an ergodic theorem of H. Weyl. We prove that many classes of solutions (a_{n})_{n≥0} of linear recurrence relations do satisfy Benford’s Law, as well as all their subsequences of the form (a_{Q(n)})_{n≥0}, where Q(n) is any non constant polynomial such that Q(n)≥0 for every n≥0. The proof rests on H. Weyl’s celebrated ”Gleichverteilung von Zahlen mod 1” Theorem.
Bibtex:
@article {,
AUTHOR = {Jolissaint, Paul},
TITLE = {Loi de Benford, relations de récurrence et suites équidistribuées},
JOURNAL = {Elem. Math.},
YEAR = {2005},
VOLUME = {60},
PAGES = {10--18},
}
Reference Type: Journal Article
Subject Area(s): Analysis