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An application of Fourier series to the most significant digit problem. (English) Zbl 0821.60045
Using Fourier series expansion and especially Parseval’s formula, the author proves some well-known theorems on the uniform distribution of sums (mod 1) of independent random variables. The author wishes to show that the log distribution is the limiting distribution when random variables are repeatedly multiplied, divided, or raised to integer powers. But for the intended application to Benford’s law, assertions on sums of random variables are more important because every arithmetic expression can be written as a sum but not as a product, in general, cf. e.g. the reviewer [J. Inf. Process. Cybern. 24, No. 9, 443-455 (1988; Zbl 0662.65040)].

MSC:
60F99 Limit theorems in probability theory
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
11K06 General theory of distribution modulo \(1\)
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