Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter May 8, 2014

A note on the Dirichlet characters of polynomials

  • Wenpeng Zhang EMAIL logo and Tingting Wang
From the journal Mathematica Slovaca

Abstract

The main purpose of this paper is using the analytic methods and the properties of character sums to study the computational problem of several kind character sums of polynomials mod q, an odd square-full number, and give two interesting identities for them.

[1] APOSTOL, T. M.: Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976. 10.1007/978-1-4757-5579-4Search in Google Scholar

[2] BURGESS, D. A.: On character sums and primitive roots, Proc. London Math. Soc. 12 (1962), 179–192. http://dx.doi.org/10.1112/plms/s3-12.1.17910.1112/plms/s3-12.1.179Search in Google Scholar

[3] BURGESS, D. A.: On Dirichlet characters of polynomials, Proc. London Math. Soc. 13 (1963), 537–548. http://dx.doi.org/10.1112/plms/s3-13.1.53710.1112/plms/s3-13.1.537Search in Google Scholar

[4] IRELAND, K.— ROSEN, M.: A classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982. http://dx.doi.org/10.1007/978-1-4757-1779-210.1007/978-1-4757-1779-2Search in Google Scholar

[5] SMITH, R. A.: On n-dimensional Kloosterman sums, J. Number Theory 11 (1979), 324–343. http://dx.doi.org/10.1016/0022-314X(79)90006-410.1016/0022-314X(79)90006-4Search in Google Scholar

[6] YE, Y.: Estimation of exponential sums of polynomials of higher degrees II, Acta Arith. 93 (2000), 221–235. 10.4064/aa-93-3-221-235Search in Google Scholar

[7] ZHANG WENPENG— YI YUAN: On Dirichlet characters of polynomials, Bull. London Math. Soc. 34 (2002), 469–473. http://dx.doi.org/10.1112/S002460930100871210.1112/S0024609301008712Search in Google Scholar

[8] ZHANG WENPENG— YAO WEILI: A note on the Dirichlet characters of polynomials, Acta Arith. 115 (2004), 225–229. http://dx.doi.org/10.4064/aa115-3-310.4064/aa115-3-3Search in Google Scholar

Published Online: 2014-5-8
Published in Print: 2014-4-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 28.3.2024 from https://www.degruyter.com/document/doi/10.2478/s12175-014-0204-z/html
Scroll to top button