Skip to main content

The rate of growth of moments of certain cotangent sums

Abstract

We consider cotangent sums associated to the zeros of the Estermann zeta function considered by the authors in their previous paper (Maier and Rassias, Generalizations of a cotangent sum associated to the Estermann zeta function, 2014). We settle a question on the rate of growth of the moments of these cotangent sums left open in Maier and Rassias (Generalizations of a cotangent sum associated to the Estermann zeta function, 2014), and obtain a simpler proof of the equidistribution of these sums.

This is a preview of subscription content, access via your institution.

References

  1. Bettin, S.: On the distribution of a cotangent sum. Int. Math. Res. Not. (2015). doi:10.1093/imrn/rnv036

  2. Billingsley P.: Probability and Measure. Wiley, New York (1995)

    MATH  Google Scholar 

  3. de la Bretèche R., Tenenbaum G.: Séries trigonométriques à coefficients arithmétiques. J. Anal. Math. 92, 1–79 (2004)

    MathSciNet  Article  MATH  Google Scholar 

  4. Harman G.: Metric Number Theory. Oxford University Press, Oxford, New York (1998)

    MATH  Google Scholar 

  5. Hensley D.: Continued Fractions. World Scientific Publ. Co., Singapore (2006)

    Book  MATH  Google Scholar 

  6. Maier, H., Rassias, M.Th.: Generalizations of a cotangent sum associated to the Estermann zeta function (2014, preprint). arXiv:1410.2145

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Th. Rassias.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Maier, H., Rassias, M.T. The rate of growth of moments of certain cotangent sums. Aequat. Math. 90, 581–595 (2016). https://doi.org/10.1007/s00010-015-0361-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-015-0361-3

Mathematics Subject Classification

  • 26A12
  • 11L03

Keywords

  • Cotangent sums
  • series
  • equidistribution
  • Estermann zeta function
  • moments
  • continued fractions
  • measure