Functiones et Approximatio Commentarii Mathematici

Waring's problem for polynomial biquadrates over a finite field of odd characteristic

Mireille Car and Luis H. Gallardo

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Abstract

Let $q$ be a power of an odd prime $p$ and let ${k}$ be a finite field with $q$ elements. Our main result is: If $q \notin \{3,9,5,13,17,25,29\},$ every polynomial $P\in{k}[t]$ of degree $\geq 269$ is a strict sum of 11 biquadrates. We first decompose $P$ as a strict mixed sum of biquadrates.

Article information

Source
Funct. Approx. Comment. Math., Volume 37, Number 1 (2007), 39-50.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229618740

Digital Object Identifier
doi:10.7169/facm/1229618740

Mathematical Reviews number (MathSciNet)
MR2357308

Zentralblatt MATH identifier
1144.11084

Subjects
Primary: 11T55: Arithmetic theory of polynomial rings over finite fields
Secondary: 11P05: Waring's problem and variants 11D85: Representation problems [See also 11P55]

Keywords
Waring's problem biquadrates polynomials finite fields odd characteristic

Citation

Car, Mireille; Gallardo, Luis H. Waring's problem for polynomial biquadrates over a finite field of odd characteristic. Funct. Approx. Comment. Math. 37 (2007), no. 1, 39--50. doi:10.7169/facm/1229618740. https://projecteuclid.org/euclid.facm/1229618740


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