J Austral Math Soc Ser A 49 pp258--263, 1990.

Normality of Some p-adic Product Expansions

Arnold Knopfmacher and John Knopfmacher

Abstract

We consider two unique products

x = ¥ Õ n=1  (1 + anpn),    x = ¥ Õ n=1  (1 + pn)bn

for a given p-adic integer x with leading coefficient 1, where a_n, b_n Î {0, 1, ..., p - 1}. It is shown that, for almost all such x relative to Haar measure on the p-adic integers, the sequences (a_n), (b_n) are normal to base p, and have standard normal distribution functions.

1980 AMS Subject Classification (1985 Revision): 11K41, 11K55

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Authors

Arnold Knopfmacher

Department of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa.

John Knopfmacher

Department of Mathematics, University of the Witswatersrand, Johannesburg, Wits 2050, South Africa.