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On some Diophantine fourier series

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Abstract

We continue our study on arithmetical Fourier series by considering two Fourier series which are related to Diophantine analysis. The first one was studied by Hardy and Littlewood in connection with the classification of numbers and the second one was studied by Hartman and Wintner by Lebesgue integration theory.

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Authors and Affiliations

  1. Department of Mathematics, Weinan Teachers University, Weinan, 714000, P. R. China

    Hai Long Li

  2. Department of Mathematics, Jilin University, Changchun, 130012, P. R. China

    Jing Ma

  3. Department of Mathematics, Northwest University, Xi’an, 710069, P. R. China

    Wen Peng Zhang

Authors
  1. Hai Long Li
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  2. Jing Ma
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  3. Wen Peng Zhang
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Correspondence to Hai Long Li.

Additional information

The first author is supported in part by NFSC Grant for Fundamental Research (No. 10671155) and NSF of Shaanxi Province (No. SJ08A22); the second author is supported in part by NNSF of China (Grant No. 10726051)

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Li, H.L., Ma, J. & Zhang, W.P. On some Diophantine fourier series. Acta. Math. Sin.-English Ser. 26, 1125–1132 (2010). https://doi.org/10.1007/s10114-010-8387-x

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  • DOI: https://doi.org/10.1007/s10114-010-8387-x

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