Pure gaps on curves with many rational places

摘要

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. (C) 2018 Elsevier Inc. All rights reserved.