Lagarias, JC and Soundararajan, K (2006). Benford's law for the 3x+1 function. Journal of the London Mathematical Society 74, pp. 289-303.
This work cites the following items of the Benford Online Bibliography:
Benford, F (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, Vol. 78, No. 4 (Mar. 31, 1938), pp. 551-572.
|
|
|
|
|
Berger, A (2005). Multi-dimensional dynamical systems and Benford's law. Discrete and Continuous Dynamical Systems 13(1), pp. 219-237. ISSN/ISBN:1078-0947. DOI:10.3934/dcds.2005.13.219.
|
|
|
|
|
Berger, A, Bunimovich, LA and Hill, TP (2005). One-dimensional dynamical systems and Benford's law. Transactions of the American Mathematical Society 357(1), pp. 197-219. ISSN/ISBN:0002-9947. DOI:10.1090/S0002-9947-04-03455-5.
|
|
|
|
|
Diaconis, P (1977). The Distribution of Leading Digits and Uniform Distribution Mod 1. Annals of Probability 5(1), pp. 72-81. ISSN/ISBN:0091-1798.
|
|
|
|
|
Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651.
|
|
|
|
|
Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363. ISSN/ISBN:0883-4237.
|
|
|
|
|
Hill, TP (1995). Base-Invariance Implies Benford's Law. Proceedings of the American Mathematical Society 123(3), pp. 887-895. ISSN/ISBN:0002-9939. DOI:10.2307/2160815.
|
|
|
|
|
Kontorovich, AV and Miller, SJ (2005). Benford's Law, Values of L-functions and the 3x+ 1 Problem. Acta Arithmetica 120(3), pp. 269-297. ISSN/ISBN:0065-1036. DOI:10.4064/aa120-3-4.
|
|
|
|
|
Kuipers, L and Niederreiter, H (1974). Uniform Distribution of Sequences. J. Wiley; newer edition - 2006 from Dover. ISSN/ISBN:0486450198.
|
|
|
|
|
Newcomb, S (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics 4(1), pp. 39-40. ISSN/ISBN:0002-9327. DOI:10.2307/2369148.
|
|
|
|
|