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The discrepancy of Farey series

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Abstract

We study the uniform distribution modulo one of the Farey series in an arbitrary subinterval of the closed unit interval [0, 1], whose fractions have denominators streaming in a given arithmetic progression, and we establish upper and lower bounds for the discrepancy of the Farey series. The distribution is closely related to the growth of the Mertens function and follows from a concise formula.

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Acknowledgement

The author express his sincere gratitude to Professor Alexandru Zaharescu for drawing this problem to his attention. He also wishes to convey his deep appreciation to the anonymous referee for carefully reading the original version of this paper and for making a number of very useful comments and suggestions which helped to improve the paper.

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  1. Department of Mathematics, University of Tennessee at Chattanooga, 415 EMCS Building, 615 McCallie Avenue, Chattanooga, Tennessee, 37403, USA

    A. H. Ledoan

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  1. A. H. Ledoan
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Ledoan, A.H. The discrepancy of Farey series. Acta Math. Hungar. 156, 465–480 (2018). https://doi.org/10.1007/s10474-018-0868-x

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  • DOI: https://doi.org/10.1007/s10474-018-0868-x

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