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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
오류제보하기
Let q be a power of 16. Every polynomial P 2 F_q[t] is a strict
sum
P = A^2 + A + B^3 + C^3 + D^3 + E^3.
The values of A,B,C,D,E are effectively obtained from the coefficients
of P. The proof uses the new result that every polynomial Q ∈ F_q[t],
satisfying the necessary condition that the constant term Q(0) has zero
trace, has a strict and effective representation as:
Q = F^2 + F + tG^2.
This improves for such q’ and such Q’ a result of Gallardo, Rahavandrainy,
and Vaserstein that requires three polynomials F, G,H for the
strict representation Q = F^2+F +GH. Observe that the latter representation
may be considered as an analogue in characteristic 2 of the strict
representation of a polynomial Q by three squares in odd characteristic.
목차
등록된 정보가 없습니다.
참고문헌 (9)
참고문헌 신청
E.Artin / 1957 / Geometric Algebra / Wiley (Interscience)
L. H. Gallardo / 2000 / the restricted Waring problem over F2n[t] / Acta Arith 92 (2) : 109 ~ 113
L. H. Gallardo / 2005 / Waring’s problem for cubes and squares over a finite field of even characteristic / Bull. Belg. Math. Soc. Simon Stevin 12 (3) : 349 ~ 362
L. H. Gallardo / 2007 / Every sum of cubes in F2[t] is a strict sum of 6 cubes / Fields Appl 13 (4) : 981 ~ 987
L. H. Gallardo / 2007 / Representations of polynomials over finite fields of characteristic two as A2 + A + BC + D3 / Finite Fields Appl 13 (3) : 648 ~ 658
L. H. Gallardo / 2000 / the restricted Waring problem over F2n[t] / Acta Arith 92 (2) : 109 ~ 113
L. H. Gallardo / 2005 / Waring’s problem for cubes and squares over a finite field of even characteristic / Bull. Belg. Math. Soc. Simon Stevin 12 (3) : 349 ~ 362
L. H. Gallardo / 2007 / Every sum of cubes in F2[t] is a strict sum of 6 cubes / Fields Appl 13 (4) : 981 ~ 987
L. H. Gallardo / 2007 / Representations of polynomials over finite fields of characteristic two as A2 + A + BC + D3 / Finite Fields Appl 13 (3) : 648 ~ 658
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