Skip to main content
SpringerLink
Log in

Bounds of trilinear sums with Kloosterman fractions

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

We obtain a new bound for trilinear exponential sums with Kloosterman fractions which in some ranges of parameters improves that of S. Bettin and V. Chandee (2018). We also obtain a similar result for more general sums.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Banks, W.D., Shparlinski, I.E.: Fractional parts of Dedekind sums. Int. J. Number Theory 112, 1137–1147 (2016)

    Article  MathSciNet  Google Scholar 

  2. Bettin, S., Chandee, V.: Trilinear forms with Kloosterman fractions. Adv. Math. 328, 1234–1262 (2018)

    Article  MathSciNet  Google Scholar 

  3. Bettin, S., Chandee, V., Radziwiłł, M.: The mean square of the product of the Riemann zeta-function with Dirichlet polynomials. J. Reine Angew. Math. 1729, 51–79 (2017)

    MathSciNet  MATH  Google Scholar 

  4. de Bruijn, N.G.: On the number of positive integers \(\le x\) and free of prime factors \(>y\), II. Indag. Math. 28, 239–247 (1966)

    Article  MathSciNet  Google Scholar 

  5. Iwaniec, H., Kowalski, E.: Analytic Number Theory. American Mathematical Society, Providence (2004)

    MATH  Google Scholar 

  6. Pappalardi, F., Sha, M., Shparlinski, I.E., Stewart, C.L.: On multiplicatively dependent vectors of algebraic numbers. Trans. Amer. Math. Soc. 370, 6221–6244 (2018)

    Article  MathSciNet  Google Scholar 

  7. Shparlinski, I.E.: On sums of Kloosterman and Gauss sums. Trans. Amer. Math. Soc. 371, 8679–8697 (2019)

    Article  MathSciNet  Google Scholar 

  8. Wu, X.: The twisted mean square and critical zeros of Dirichlet \(L\)-functions. Math. Z. 293, 825–865 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author is very grateful to the anonymous referee for the very careful reading of the manuscript and valuable comments. This work was supported by the Australian Research Council Grant DP170100786.

Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia

    Igor E. Shparlinski

Authors
  1. Igor E. Shparlinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Igor E. Shparlinski.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shparlinski, I.E. Bounds of trilinear sums with Kloosterman fractions. Arch. Math. 117, 261–266 (2021). https://doi.org/10.1007/s00013-021-01623-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-021-01623-y

Mathematics Subject Classification

Keywords

Search

Navigation