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Deligny, H and Jolissaint, P (2013)

Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]

Elemente der Mathematik, 68(1), pp. 9-21.

ISSN/ISBN: Not available at this time. DOI: 10.4171/EM/213

Note - this is a foreign language paper: FRE



Abstract: A sequence of positive numbers (a_n) satisfies Benford's Law if, for every digit d between 1 and 9, the proportion of values of the indices n for which a_n has d as first digit is equal to log_{10}(1+1/d). In two previous articles, the second co-author studied sequences (a_n) that satisfy linear recurrence equations of the form a_{n+k}=c_{k-1}a_{n+k-1}+c_{k-2}a_{n+k-2}+\ldots+c_1a_{n+1}+c_0a_n, and he provided sufficient conditions on the roots of the characteristic polynomial p(x)=x^k-c_{k-1}x^{k-1}-\ldots-c_1x-c_0 of the relation that ensure that (a_n) satisfies Benford's Law. Here, we give sufficient conditions directly on the coefficients c_0,...,c_{k-1} in order that solutions of such recurrence relations satisfy the same law. Emphasis is put on many cases where the coefficients are non negative real numbers.


Bibtex:
@article {, AUTHOR = {Hugues Deligny and Paul Jolissaint}, TITLE = {Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]}, JOURNAL = {Elemente der Mathematik}, YEAR = {2013}, VOLUME = {68}, NUMBER = {1}, PAGES = {9--21}, DOI = {10.4171/EM/213}, URL = {http://www.ems-ph.org/journals/show_abstract.php?issn=0013-6018&vol=68&iss=1&rank=2}, }


Reference Type: Journal Article

Subject Area(s): Analysis, Dynamical Systems