Benford Solutions of Linear Difference Equations

  • Arno BergerEmail author
  • Gideon Eshun
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 102)


Benford’s Law (BL), a notorious gem of mathematics folklore, asserts that leading digits of numerical data are usually not equidistributed, as might be expected, but rather follow one particular logarithmic distribution. Since first recorded by Newcomb in 1881, this apparently counter-intuitive phenomenon has attracted much interest from scientists and mathematicians alike. This article presents a comprehensive overview of the theory of BL for autonomous linear difference equations. Necessary and sufficient conditions are given for solutions of such equations to conform to BL in its strongest form. The results extend and unify previous results in the literature. Their scope and limitations are illustrated by numerous instructive examples.


Linear Difference Equations Logarithmic Distribution Skolem Mahler Lech Theorem Jordan Normal Form Theorem Significand 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by an Nserc Discovery Grant. The authors are grateful to T. Hill, A. Weiss, and R. Zweimüller for helpful conversations.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of AlbertaEdmontonCanada

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