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Linked References

1. S. Newcomb, “Note on the frequency of use of the different digits in natural numbers,” American Journal of Mathematics, vol. 4, no. 1–4, pp. 39–40, 1881. View at Publisher · View at Google Scholar · View at MathSciNet
2. F. Benford, “The law of anomalous numbers,” Proceedings of the American Philosophical Society, vol. 78, pp. 551–572, 1938. View at Zentralblatt MATH
3. R. S. Pinkham, “On the distribution of first significant digits,” Annals of Mathematical Statistics, vol. 32, pp. 1223–1230, 1961. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
4. D. I. A. Cohen, “An explanation of the first digit phenomenon,” Journal of Combinatorial Theory. Series A, vol. 20, no. 3, pp. 367–370, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
5. T. P. Hill, “Base-invariance implies Benford's law,” Proceedings of the American Mathematical Society, vol. 123, no. 3, pp. 887–895, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. T. P. Hill, “The significant-digit phenomenon,” The American Mathematical Monthly, vol. 102, no. 4, pp. 322–327, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. T. P. Hill, “A statistical derivation of the significant-digit law,” Statistical Science, vol. 10, no. 4, pp. 354–363, 1995. View at Zentralblatt MATH · View at MathSciNet
8. T. P. Hill, “Benford's law,” Encyclopedia of Mathematics Supplement, vol. 1, p. 102, 1997.
9. T. P. Hill, “The first digit phenomenon,” The American Scientist, vol. 86, no. 4, pp. 358–363, 1998.
10. P. C. Allaart, “An invariant-sum characterization of Benford's law,” Journal of Applied Probability, vol. 34, no. 1, pp. 288–291, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
11. É. Janvresse and T. de la Rue, “From uniform distributions to Benford's law,” Journal of Applied Probability, vol. 41, no. 4, pp. 1203–1210, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
12. A. E. Kossovsky, “Towards a better understanding of the leading digits phenomena,” preprint, 2008, http://arxiv.org/abs/math/0612627.
13. D. Jang, J. U. Kang, A. Kruckman, J. Kudo, and S. J. Miller , “Chains of distributions, hierarchical Bayesian models and Benford's law,” Journal of Algebra, Number Theory: Advances and Applications, vol. 1, no. 1, pp. 37–60, 2009.
14. S. J. Miller and M. J. Nigrini, “The modulo 1 central limit theorem and Benford's law for products,” International Journal of Algebra, vol. 2, no. 1–4, pp. 119–130, 2008. View at Zentralblatt MATH · View at MathSciNet
15. O. Kafri, “Entropy principle in direct derivation of Benford's law,” preprint, 2009, http://arxiv.org/ftp/arxiv/papers/0901/0901.3047.pdf.
16. W. Hürlimann, “Benford's law from 1881 to 2006: a bibliography,” 2006, http://arxiv.org/abs/math/0607168.
17. A. Berg and T. Hill, “Benford Online Bibliography,” 2009, http://www.benfordonline.net.
18. G. Judge and L. Schechter, “Detecting problems in survey data using Benford's law,” Journal of Human Resources, vol. 44, no. 1, pp. 1–24, 2009. View at Publisher · View at Google Scholar
19. G. Judge, L. Schechter, and M. Grendar, “An information theoretic family of data based Benford-like distributions,” Physica A, vol. 97, pp. 201–207, 2007.
20. M. J. Nigrini and S. J. Miller, “Benford's law applied to hydrology data—results and relevance to other geophysical data,” Mathematical Geology, vol. 39, no. 5, pp. 469–490, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. L. M. Leemis, B. W. Schmeiser, and D. L. Evans, “Survival distributions satisfying Benford's law,” The American Statistician, vol. 54, no. 4, pp. 236–241, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
22. H.-A. Engel and C. Leuenberger, “Benford's law for exponential random variables,” Statistics & Probability Letters, vol. 63, no. 4, pp. 361–365, 2003. View at Zentralblatt MATH · View at MathSciNet
23. J. R. van Dorp and S. Kotz, “The standard two-sided power distribution and its properties: with applications in financial engineering,” The American Statistician, vol. 56, no. 2, pp. 90–99, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
24. W. Hürlimann, “A generalized Benford law and its application,” Advances and Applications in Statistics, vol. 3, no. 3, pp. 217–228, 2003. View at Zentralblatt MATH · View at MathSciNet
25. W. J. Reed, “The Pareto, Zipf and other power laws,” Economics Letters, vol. 74, no. 1, pp. 15–19, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
26. A. V. Kontorovich and S. J. Miller, “Benford's law, values of $L$-functions and the $3x+1$ problem,” Acta Arithmetica, vol. 120, no. 3, pp. 269–297, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
27. K. Schürger, “Extensions of Black-Scholes processes and Benford's law,” Stochastic Processes and Their Applications, vol. 118, no. 7, pp. 1219–1243, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
28. O. Kafri, “The second law as a cause of the evolution,” preprint, 2007, http://arxiv.org/ftp/arxiv/papers/0711/0711.4507.pdf.
29. O. Kafri, “Sociological inequality and the second law,” preprint, 2008, http://arxiv.org/ftp/arxiv/papers/0805/0805.3206.pdf.
30. J. L. Brown Jr. and R. L. Duncan, “Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences,” The Fibonacci Quarterly, vol. 8, no. 5, pp. 482–486, 1970. View at Zentralblatt MATH · View at MathSciNet
31. J. Wlodarski, “Fibonacci and Lucas numbers tend to obey Benford's law,” The Fibonacci Quarterly, vol. 9, pp. 87–88, 1971.
32. W. A. Sentance, “A further analysis of Benford's law,” The Fibonacci Quarterly, vol. 11, pp. 490–494, 1973. View at Zentralblatt MATH
33. W. Webb, “Distribution of the first digits of Fibonacci numbers,” The Fibonacci Quarterly, vol. 13, no. 4, pp. 334–336, 1975. View at Zentralblatt MATH · View at MathSciNet
34. R. A. Raimi, “The first digit problem,” American Mathematical Monthly, vol. 83, pp. 521–538, 1976.
35. W. G. Brady, “More on Benford's law,” The Fibonacci Quarterly, vol. 16, pp. 51–52, 1978. View at Zentralblatt MATH
36. S. Kunoff, “$N$! has the first digit property,” The Fibonacci Quarterly, vol. 25, no. 4, pp. 365–367, 1987. View at Zentralblatt MATH · View at MathSciNet
37. S. J. Miller and R. Takloo-Bighash, An Invitation to Modern Number Theory, Princeton University Press, Princeton, NJ, USA, 2006. View at MathSciNet
38. P. Jolissaint, “Loi de Benford, relations de récurrence et suites équidistribuées,” Elemente der Mathematik, vol. 60, no. 1, pp. 10–18, 2005. View at Zentralblatt MATH · View at MathSciNet
39. P. Jolissaint, “Loi de Benford, relations de récurrence et suites équidistribuées. II,” Elemente der Mathematik, vol. 64, no. 1, pp. 21–36, 2009. View at MathSciNet
40. W. Hürlimann, “Integer powers and Benford's law,” International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 39–46, 2004. View at Zentralblatt MATH · View at MathSciNet
41. P. Diaconis, “The distribution of leading digits and uniform distribution mod 1,” Annals of Probability, vol. 5, pp. 72–81, 1977.
42. R. E. Whitney, “Initial digits for the sequence of primes,” The American Mathematical Monthly, vol. 79, no. 2, pp. 150–152, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
43. P. Schatte, “On $H_{\infty }$-summability and the uniform distribution of sequences,” Mathematische Nachrichten, vol. 113, pp. 237–243, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
44. D. I. A. Cohen and T. M. Katz, “Prime numbers and the first digit phenomenon,” Journal of Number Theory, vol. 18, no. 3, pp. 261–268, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
45. J.-P. Serre, A Course in Arithmetic, Springer, New York, NY, USA, 1996.