Let K be an algebraically closed field, and let F/K (x) be a Kummer extension of function fields of genus g. We provide a compact and explicit description of the gap set G (Q) at any totally ramified place Q of the extension F/K (x). As a consequence, we deduce structural properties of the Weierstrass semigroup H (Q) ; in particular, we determine a generating set for H (Q), and we characterize its symmetry in certain cases. We also generalize a formula due to Towse that describes the asymptotic behavior of the sum of the Weierstrass weights at all totally ramified places of the extension F/K (x) relative to g³-g.
Cotterill et al. (Mon,) studied this question.
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