For an algebraic curve [Formula: see text] defined over an algebraically closed field of characteristic [Formula: see text], [Formula: see text]-number [Formula: see text] is the dimension of the space of exact holomorphic differentials on [Formula: see text]. We computed the [Formula: see text]-number for a family of certain Picard curves using the action of the Cartier operator on [Formula: see text].
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Nourozi et al. (2024) studied this question.
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