Geodesic
On the distribution of fractional parts and Benford's law
Izvestiya. Mathematics, Tome 19 (1982) no. 1, pp. 65-77 
A. I. Pavlov. On the distribution of fractional parts and Benford's law. Izvestiya. Mathematics, Tome 19 (1982) no. 1, pp. 65-77. http://geodesic.mathdoc.fr/item/IM2_1982_19_1_a4/
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     title = {On~the distribution of fractional parts and {Benford's} law},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article investigates the distribution of the first digits (from the left) in the $q$-nary expansions of numerical sequences and functions ($q$ an integer $\geqslant2$). Bibliography: 13 titles.

[1] Benford F., “The law of anomalous numbers”, Proc. Amer. Philos. Soc., 78 (1938), 551–572 | Zbl

[2] Nechaev V. I., Chislovye sistemy, Prosveschenie, M., 1975

[3] Flehinger B. J., “On the probability that a random has initial digit $A$”, Amer. Mathem. Month., 73 (1966), 1056–1061 | DOI | MR | Zbl

[4] Raimi R. A., “On the distribution of first significant figurs”, Amer. Mathem. Month., 76 (1969), 342–348 | DOI | MR | Zbl

[5] Pinkham R. S., “On the distribution of first significant digits”, Ann. Math. Statist., 32 (1961), 1223–1230 | DOI | MR | Zbl

[6] Konheim. A. G., “Mantissa Distributions”, Mathem. Comput., 19 (1965), 143–144 | DOI | MR | Zbl

[7] Knut D., Iskusstvo programmirovaniya dlya EVM, t. 2, Mir, M., 1977 | Zbl

[8] Vinogradov I. M., “Ob otsenke trigonometricheskikh summ s prostymi chislami”, Izv. AN SSSR. Ser. matem., 12 (1948), 225–248 | MR | Zbl

[9] van der Corput I. G., “Diophantische Ungleichungen. I: Zur Gleichverteilung modulo Eins”, Acta Math., 56 (1931), 373–456 | DOI | MR | Zbl

[10] Weyl H., “Über die Gleichverteilung von Zahlen modulo Eins”, Math. Ann., 77 (1916), 313–352 | DOI | MR | Zbl

[11] Ingam A. E., Raspredelenie prostykh chisel, ONTI, M., L., 1936

[12] Kassels D. V., Vvedenie v teoriyu diofantovykh priblizhenii, IL, M., 1961

[13] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1971 | MR