Sums and strict sums of biquadrates in Fq[t],qε{3,9}

Luis H. Gallardo, Leonid N. Vaserstein

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Let q be a power of a prime number. Observe that just for q ε {3,9} some congruence obstructions occur to the representation of polynomials in Fq[t] as a sum (and so also as a strict sum) of biquadrates. We define g(4,Fq[t}) as the least g such that every polynomial that is a strict sum of biquadrates is a strict sum of g biquadrates. We compare the set of sums of biquadrates with the set of strict sums of biquadrates for q ε {3,9}. Our main result is that g(4,Fq[t]) ≤14 when q ε {3,9}. The set of sums of cubes in F4[t] is also determined. This completes the study of the case of representation by sums of cubes (in which the congruence obstructions occur only for 9 ε{2,4}).

Original languageEnglish (US)
Pages (from-to)1863-1874
Number of pages12
JournalRocky Mountain Journal of Mathematics
Issue number6
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • General Mathematics


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