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On the high-th power mean of one kind general Kloosterman sums

  • Wenpeng ZhangEmail author
  • Jiayuan Hu
Original Paper
  • 89 Downloads

Abstract

The main purpose of this paper is using the analytic methods and a relation between the two-term cubic exponential sums and general Kloosterman sums to study the computational problem of one kind high-th power mean of general Kloosterman sums for some special non-principal character \(\chi \bmod p\), and give four exact computational formulae for them. As applications of these results, we obtained four interesting asymptotic formulae for the 6th, 8th, 10th and 12th power mean of general Kloosterman sums with a special character \(\chi \bmod p\).

Keywords

Kloosterman sums High-th power mean Identity Asymptotic formula 

Mathematics Subject Classification

11L03 11L05 

Notes

Acknowledgements

The authors would like to thank the referees for their very helpful and detailed comments, which have significantly improved the presentation of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.School of MathematicsNorthwest UniversityXi’anPeople’s Republic of China

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