O ct 2 00 4 On the Existence of Non - Special Divisors of Degree g and g − 1 in Algebraic Function Fields over
نویسنده
چکیده
We study the existence of non-special divisors of degree g and g − 1 for algebraic function fields of genus g ≥ 1 defined over a finite field Fq. In particular, we prove that there always exists an effective non-special divisor of degree g ≥ 2 if q ≥ 3 and that there always exists a non-special divisor of degree g − 1 ≥ 1 if q ≥ 4. We use our results to improve upper and upper asymptotic bounds on the bilinear complexity of the multiplication in any extension Fqn of Fq, when q = 2r ≥ 16. 2000 Mathematics Subject Classification: 11R58.
منابع مشابه
1 3 O ct 2 00 4 On the Existence of Non - Special Divisors of Degree g and g − 1 in Algebraic Function Fields over F q
We study the existence of non-special divisors of degree g and g − 1 for algebraic function fields of genus g ≥ 1 defined over a finite field Fq. In particular, we prove that there always exists an effective non-special divisor of degree g ≥ 2 if q ≥ 3 and that there always exists a non-special divisor of degree g − 1 ≥ 1 if q ≥ 4. We use our results to improve upper and upper asymptotic bounds...
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Let Mg,2 be the moduli space of curves of genus g with a level2 structure. We prove here that there is always a non hyperelliptic element in the intersection of four thetanull divisors in M6,2. We prove also that for all g > 3, each component of the hyperelliptic locus in Mg,2 is a connected component of the intersection of g − 2 thetanull divisors.
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Let Mg,2 be the moduli space of curves of genus g with a level2 structure. We prove here that there is always a non hyperelliptic element in the intersection of four thetanull divisors in M6,2. We prove also that for all g > 3, each component of the hyperelliptic locus in Mg,2 is a connected component of the intersection of g − 2 thetanull divisors.
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