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. | ||||
Boyle, J (1994). An Application of Fourier Series to the Most Significant Digit Problem. American Mathematical Monthly 101(9), pp. 879-886. ISSN/ISBN:0002-9890. DOI:10.2307/2975136. | ||||
Cigler, J and Helmberg, G (1961). Neuere Entwicklungen der Theorie der Gleichverteilung. Jahresbericht der Deutschen Mathematiker Vereinigung 64, pp. 1-50. GER | ||||
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. | ||||
Flehinger, BJ (1966). On the Probability that a Random Integer has Initial Digit A. American Mathematical Monthly 73(10), pp. 1056-1061. ISSN/ISBN:0002-9890. DOI:10.2307/2314636. | ||||
Fuchs, A and Letta, G (1996). Le problème du premier chiffre décimal pour les nombres premiers. The Electronic Journal of Combinatorics 3(2), R25. FRE | ||||
Giuliano-Antonini, R (1991). On the notion of uniform distribution mod 1. Fibonacci Quarterly 29(3), pp. 230-234. | ||||
Goto, K (1992). Some examples of Benford sequences. Mathematical Journal of the Okayama University 34, pp. 225-232. | ||||
Hill, TP (1995). The Significant-Digit Phenomenon. American Mathematical Monthly 102(4), pp. 322-327. DOI:10.2307/2974952. | ||||
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. | ||||
Jager, H and Liardet, P (1988). Distribution arithmétiques des dénominateurs de convergents de fractions continues. Nederl. Akad. Wetensch. Indag. Math. 50(2), pp. 181-197. DOI:10.1016/S1385-7258(88)80026-X. FRE | ||||
Jech, T (1992). The Logarithmic Distribution of Leading Digits and Finitely Additive Measures. Discrete Mathematics 108(1-3), pp. 53-57. ISSN/ISBN:0012-365X. DOI:10.1016/0012-365X(92)90659-4. | ||||
Kanemitsu, S, Nagasaka, K, Rauzy, G and Shiue, JS (1988). On Benford’s law: the first digit problem. Lecture Notes in Mathematics 1299, pp. 158-169 (eds. Watanabe, S, and Prokhorov, YV). ISSN/ISBN:978-3-540-18814-8. DOI:10.1007/BFb0078471. | ||||
Katz, TM and Cohen, DIA (1986). The first digit property for exponential sequences is independent of the underlying distribution. Fibonacci Quarterly 24(1), pp. 2-7. | ||||
Knuth, DE (1997). The Art of Computer Programming. pp. 253-264, vol. 2, 3rd ed, Addison-Wesley, Reading, MA. | ||||
Konheim, AG (1965). Mantissa distribution. Mathematics of Computation 19, pp. 143-144. DOI:10.1090/S0025-5718-1965-0175159-1. | ||||
Kuipers, L and Niederreiter, H (1974). Uniform Distribution of Sequences. J. Wiley; newer edition - 2006 from Dover. ISSN/ISBN:0486450198. | ||||
Kuipers, L and Shiue, JS (1973). Remark on a paper by Duncan and Brown on the sequence of logarithms of certain recursive sequences. Fibonacci Quarterly 11(3), pp. 292-294. | ||||
Kunoff, S (1987). N! has the first digit property. Fibonacci Quarterly 25, pp. 365-367. | ||||
Nagasaka, K, Kanemitsu, S and Shiue, JS (1990). Benford’s law: The logarithmic law of first digit. In: Győry, K, Halász, G. (eds.) Number theory. Vol. I. Elementary and analytic, Proc. Conf., Budapest/Hung. 1987, Colloq. Math. Soc. János Bolyai 51, pp. 361-391 . | ||||
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. | ||||
Niederreiter, H and Philipp, W (1973). Berry-Esseen bounds and a theorem of Erdős and Turàn on uniform distribution mod 1. Duke Mathematical Journal 40(3), 633-649. DOI:10.1215/S0012-7094-73-04055-6. | ||||
Pinkham, RS (1961). On the Distribution of First Significant Digits. Annals of Mathematical Statistics 32(4), pp. 1223-1230. ISSN/ISBN:0003-4851. | ||||
Raimi, RA (1969). On Distribution of First Significant Figures. American Mathematical Monthly 76(4), pp. 342-348. ISSN/ISBN:0002-9890. DOI:10.2307/2316424. | ||||
Schatte, P (1981). On random variables with logarithmic mantissa distribution relative to several bases. Elektronische Informationsverarbeitung und Kybernetik 17(4/6), 293-295. ISSN/ISBN:0013-5712. | ||||
Schatte, P (1983). On H∞ -summability and the uniform distribution of sequences. Math. Nachr. 113, 237-243. DOI:10.1002/mana.19831130122. | ||||
Schatte, P (1984). On the asymptotic uniform distribution of sums reduced mod 1. Math. Nachr. 115, 275-281. DOI:10.1002/mana.19841150121. | ||||
Schatte, P (1986). On the Asymptotic Logarithmic Distribution of the Floating-Point Mantissas of Sums. Math. Nachr. 127, 7-20. ISSN/ISBN:0025-584X. DOI:10.1002/mana.19861250102. | ||||
Schatte, P (1987). Some estimates of the H∞ -uniform distribution. Monatshefte für Mathematik 103, 233-240. | ||||
Schatte, P (1988). On mantissa distributions in computing and Benford’s law. Journal of Information Processing and Cybernetics EIK 24(9), 443-455. ISSN/ISBN:0863-0593. | ||||
Schatte, P (1988). On the uniform distribution of certain sequences and Benford’s law. Math. Nachr. 136, 271-273. DOI:10.1002/mana.19881360119. | ||||
Schatte, P (1989). On measures of uniformly distributed sequences and Benford's law. Monatshefte für Mathematik 107(3), 245-256. ISSN/ISBN:0026-9255. DOI:10.1007/BF01300347. | ||||
Schatte, P (1990). On Benford’s law for continued fractions. Math. Nachr. 148, 137-144. DOI:10.1002/mana.3211480108. | ||||
Schatte, P (1991). On a uniform law of the iterated logarithm for sums mod 1 and Benford’s law. Lithuanian Mathematical Journal 31(1), 133-142. DOI:10.1007/BF00972327. | ||||
Schatte, P (1998). On Benford's law to variable base. Statistics & Probability Letters 37(4): 391-397. ISSN/ISBN:0167-7152. DOI:10.1016/S0167-7152(97)00142-9. | ||||
Schatte, P and Nagasaka, K (1991). A note on Benford’s law for second order linear recurrences with periodical coefficients. Z. Anal. Anwend. 10(2), pp. 251-254. | ||||
Sentance, WA (1973). A further analysis of Benford’s law. Fibonacci Quarterly 11, 490-494. | ||||
Tichy, RF (1985). Uniform distribution and diophantine inequalities. Monatsh. Math. 99(2), 147-152. ISSN/ISBN:0026-9255. DOI:10.1007/BF01304194. | ||||
Tichy, RF (1987). Gleichverteilung zum Summierungsverfahren H∞. Math. Nachr. 131(1), 119-125. DOI:10.1002/mana.19871310112. GER | ||||
Tichy, RF (1987). Statistische Resultate über computergerechte Darstellungen von Zahlen. Anzeiger der Österreichischen Akademie der Wissenschaften. Mathematisch- Naturwissenschaftliche Klasse 124, pp.1-8. GER | ||||
Too, YH (1992). On the uniform distribution modulo one of some log-like sequences. Proc. Japan Acad. A 68, 269-272. | ||||
Tsuji, M (1952). On the uniform distribution of numbers mod 1. Journal of the Mathematical Society of Japan 4(3/4), pp. 313-322. DOI:10.2969/jmsj/00430313. | ||||
Washington, LC (1981). Benford’s law for Fibonacci and Lucas numbers. Fibonacci Quarterly 19, 175-177. | ||||
Webb, W (1975). Distribution of the first digits of Fibonacci numbers. Fibonacci Quarterly 13, pp. 334-336. | ||||
Weyl, H (1916). Über die Gleichverteilung von Zahlen mod Eins. Mathematische Annalen 77, 313-352. ISSN/ISBN:0025-5831. DOI:10.1007/BF01475864. GER |