On the Waring problem with Dickson polynomials modulo a prime

Authors

DOI:

https://doi.org/10.53733/579

Keywords:

Dickson polynomials, Waring problem, Kloosterman sums, Gauss sums

Abstract

We improve recent results of D. Gomez and A. Winterhof (2010) and of A. Ostafe and I. E. Shparlinski (2011) on the Waring problem with Dickson polynomials in the case of prime finite fields. Our approach is based on recent bounds of Kloosterman and Gauss sums due to A. Ostafe, I. E. Shparlinski and J. F. Voloch (2021).

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Author Biographies

Igor E. Shparlinski, University of New South Wales

Igor Shparlinski
School of Mathematics and Statistics,
University of New South Wales,
Sydney, NSW 2052
Australia
igor.shparlinski@unsw.edu.au

José Felipe Voloch, University of Canterbury

José Felipe Voloch
School of Mathematics and Statistics,
University of Canterbury,
Private Bag 4800,
Christchurch 8140,
New Zealand
felipe.voloch@canterbury.ac.nz

 

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Published

15-07-2025

How to Cite

Shparlinski, I. E., & Voloch, J. F. (2025). On the Waring problem with Dickson polynomials modulo a prime. New Zealand Journal of Mathematics, 56, 1–13. https://doi.org/10.53733/579

Issue

Vol. 56 (2025)

Section

Articles