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Benford Solutions of Linear Difference Equations

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Theory and Applications of Difference Equations and Discrete Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 102))

Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. University of Alberta, Edmonton, AB, Canada

    Arno Berger & Gideon Eshun

Authors
  1. Arno Berger
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  2. Gideon Eshun
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Correspondence to Arno Berger .

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Editors and Affiliations

  1. Sultan Qaboos University Dept. of Math. and Statistics, Muscat, Oman

    Ziyad AlSharawi

  2. University of Arizona Dept. of Mathematics, Tucson, Arizona, USA

    Jim M. Cushing

  3. Trinity University Dept. of Mathematics, San Antonio, Texas, USA

    Saber Elaydi

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Berger, A., Eshun, G. (2014). Benford Solutions of Linear Difference Equations. In: AlSharawi, Z., Cushing, J., Elaydi, S. (eds) Theory and Applications of Difference Equations and Discrete Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44140-4_2

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