On the Existence of Dimension Zero Divisors in Algebraic Function Fields
نویسندگان
چکیده
Let F/Fq be an algebraic function field of genus g defined over a finite field Fq. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g− k in F/Fq where k is an integer ≥ 1. In particular, for q = 2, 3 we prove that there always exists a dimension zero divisor of degree γ − 1 where γ is the q-rank of F and in particular a non-special divisor of degree g − 1 when the Jacobian of F is ordinary. We also give a necessary and sufficient condition for the existence of a dimension zero divisor of degree g− k for a hyperelliptic field F in terms of its Zeta function.
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