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Quadratic Forms onF q [ T ]

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Quadratic Forms onF q [ T ]

Auteurs : Mireille Car [France]

Source :

Journal of Number Theory [ 0022-314X ] ; 1996.

RBID : ISTEX:DDF6F168E704C81FF01AB08C59934D12E9140D67

English descriptors

KwdEn :
- Absolute value, Circle method, Coprime, Divisor, Duke math, Farey, Farey ball, Farey balls, Farey fractions, Finite field, Integer, Irreducible, Irreducible divisors, Irreducible factors, Irreducible polynomial, Lop8m, Many polynomials, Mireille, Monic, Monic polynomial, Page codes, Pairwise, Pairwise coprime, Pairwise coprime polynomials, Polynomial coprime, Positive integer, Quadratic, Quadratic forms, Resp, Restrictive degree conditions, Same result, Strict representation.
Teeft :
- Absolute value, Circle method, Coprime, Divisor, Duke math, Farey, Farey ball, Farey balls, Farey fractions, Finite field, Integer, Irreducible, Irreducible divisors, Irreducible factors, Irreducible polynomial, Lop8m, Many polynomials, Mireille, Monic, Monic polynomial, Page codes, Pairwise, Pairwise coprime, Pairwise coprime polynomials, Polynomial coprime, Positive integer, Quadratic, Quadratic forms, Resp, Restrictive degree conditions, Same result, Strict representation.

Abstract

Abstract: In this paper, we study the number of representations of polynomials of the ringFq[T] by diagonal quadratic forms[formula]whereA1, …, Asare given polynomials andY1, …, Ysare polynomials subject to satisfying the most restrictive degree conditions. WhenA1, …, Asare pairwise coprime, ands⩾5, we use the ordinary circle method; whenA1, …, A4are pairwise coprime we adapt Kloosterman's method to the polynomial case and we get an asymptotic estimate for the number R(A1, …, As; M) of representations of a polynomialMas a sum(Q). We also deal with the particular cases=4,A1=A2=D,A3=A4=1, whereDis a square-free polynomial. In this particular case, the number R(A1, …, A4; M) is the number of representations ofMas a sum of two norms of elements of the quadratic extension[formula]satisfying the most restrictive degree conditions.

Url:

https://api.istex.fr/document/DDF6F168E704C81FF01AB08C59934D12E9140D67/fulltext/pdf

DOI: 10.1006/jnth.1996.0142

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">Abstract: In this paper, we study the number of representations of polynomials of the ringFq[T] by diagonal quadratic forms[formula]whereA1, …, Asare given polynomials andY1, …, Ysare polynomials subject to satisfying the most restrictive degree conditions. WhenA1, …, Asare pairwise coprime, ands⩾5, we use the ordinary circle method; whenA1, …, A4are pairwise coprime we adapt Kloosterman's method to the polynomial case and we get an asymptotic estimate for the number R(A1, …, As; M) of representations of a polynomialMas a sum(Q). We also deal with the particular cases=4,A1=A2=D,A3=A4=1, whereDis a square-free polynomial. In this particular case, the number R(A1, …, A4; M) is the number of representations ofMas a sum of two norms of elements of the quadratic extension[formula]satisfying the most restrictive degree conditions.</div>
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Quadratic Forms onF q [ T ]

Quadratic Forms onF q [ T ]

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

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