Article
On the Distribution Modulo One of the Mean Values of Some Arithmetical Functions
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Abstract
Florian Luca asked whether the sequence consisting of the arith- metic (resp. geometric) mean values of the Euler ϕ function is uniformly dis- tributed modulo 1. We show that it is the case for the arithmetic means, and thatit the case for the geometric means if and only if the number e−1 (1 − 1/p)1/p p is irrational. More general arithmetic functions are also considered.
Keywords
Euler function, distribution modulo 1, multiplicative functions.
Citation
Deshouillers, J. & Iwaniec, H. (2008). On the distribution modulo one of the mean values of some arithmetical functions. Uniform Distribution Theory, 3(1), 111–124.
J. Deshouillers and H. Iwaniec, “On the distribution modulo one of the mean values of some arithmetical functions,” Uniform Distribution Theory, vol. 3, no. 1, pp. 111–124, 2008.
Deshouillers J, Iwaniec H. On the distribution modulo one of the mean values of some arithmetical functions. Uniform Distribution Theory. 2008;3(1):111–124.
Deshouillers, J. and Iwaniec, H. (2008), ‘On the distribution modulo one of the mean values of some arithmetical functions’, Uniform Distribution Theory, 3(1), pp. 111–124.
Deshouillers, Jean-Marc, and Henryk Iwaniec. “On the Distribution Modulo One of the Mean Values of Some Arithmetical Functions.” Uniform Distribution Theory, vol. 3, no. 1, 2008, pp. 111–124.
Deshouillers, Jean-Marc, and Henryk Iwaniec. “On the Distribution Modulo One of the Mean Values of Some Arithmetical Functions.” Uniform Distribution Theory 3, no. 1 (2008): 111–124.
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Published by: Engineering Journals
