Pure gaps on curves with many rational places

04/02/2018

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by   Daniele Bartoli, et al.

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We consider the algebraic curve defined by y^m = f(x) where m ≥ 2 and f(x) is a rational function over F_q. We extend the concept of pure gap to c-gap and obtain a criterion to decide when an s-tuple is a c-gap at s rational places on the curve. As an application, we obtain many families of pure gaps at two rational places on curves with many rational places.