JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

Submit Article

THE HYBRID POWER MOMENT OF CHARACTER SUMS AND TWO-TERM EXPONENTIAL SUMS

Authors

  • Xuan Wang

Keywords:

character sums of polynomials, two-term exponential sums, asymptotic formula

DOI:

https://doi.org/10.17654/0972555525023

Abstract

This paper focuses on the investigation of the hybrid power mean concerning some special character sums of polynomials and the two-term exponential sums by utilizing analytical approaches and the nature of Gauss sums to give two sharp asymptotic formulae for them.

Received: March 30, 2025
Revised: May 6, 2025
Accepted: May 19, 2025

References

D. Han, A hybrid mean value involving two-term exponential sums and polynomial character sums, Czechoslovak Math. J 64 (2014), 53-62.

X. Y. Du, The hybrid power mean of two-term exponential sums and character sums, Acta Math. Sin. (Chin. Ser.) 59 (2016), 309-316.

W. P. Zhang and Y. Yi, On Dirichlet characters of polynomials, Bull. London Math. Soc. 34 (2002), 469-473.

D. A. Burgess, On Dirichlet characters of polynomials, Proceedings of the London Mathematical Society 13 (1963), 537-548.

Y. K. Ma and W. P. Zhang, On the two-term exponential sums and character sums of polynomials, Open Mathematics 17 (2019), 1239-1248.

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.

K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1982.

X. X. Lv and W. P. Zhang, On the character sum of polynomials and the two-term exponential sums, Acta Math. Sin. Engl. Ser. 36 (2020), 196-206.

X. X. Lv and W. P. Zhang, A new hybrid power mean involving the generalized quadratic Gauss sums and sums analogous to Kloosterman sums, Lithuanian Math. J. 57 (2017), 359-366.

Z. F. Xu, T. P. Zhang and W. P. Zhang, On the mean value of the two-term exponential sums with Dirichlet characters, J. Number Theory 123 (2007), 352-362.

W. P. Zhang, The fourth and sixth power mean of the classical Kloosterman sums, J. Number Theory 131 (2011), 228-238.

H. Zhang and W. P. Zhang, The fourth power mean of two-term exponential sums and its application, Mathematical Reports 19 (2017), 75-81.

X. Wang, L. Wang and G. H. Chen, The fourth power mean of the generalized quadratic Gauss sums associated with some Dirichlet characters, AIMS Mathematics 9 (2024), 17774-17783.

Published

2025-06-11

Issue

Section

Articles

How to Cite

THE HYBRID POWER MOMENT OF CHARACTER SUMS AND TWO-TERM EXPONENTIAL SUMS. (2025). JP Journal of Algebra, Number Theory and Applications, 64(4), 433-450. https://doi.org/10.17654/0972555525023

Similar Articles

1-10 of 40

You may also start an advanced similarity search for this article.