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arXiv · 0906.5216

On the existence of dimension zero divisors in algebraic function fields defined over F_q

Stephane Ballet·Christophe Ritzenthaler·Robert Rolland
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Abstract

Let F/F_q be an algebraic function field of genus g defined over a finite field F_q. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g-k in F where k is a positive integer. In particular, for q=2,3 we prove that there always exists a dimension zero divisor of degree \gamma-1 where \gamma is the q-rank of F. 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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Stephane Ballet, Christophe Ritzenthaler, Robert Rolland. 2009-06-29. On the existence of dimension zero divisors in algebraic function fields defined over F_q. https://doi.org/10.4064/aa143-4-4

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