We present an algorithm for counting points on superelliptic curves yr = f(x) over a finite field Fq of small characteristic different from r. This is an extension of an algorit...
Abstract. Following Gaudry and G¨urel who extended Kedlaya’s point-counting algorithm to superelliptic curves, we introduce Harvey’s running time improvements for large enough...
We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic...
We present an algorithm to compute the zeta function of an arbitrary hyperelliptic curve over a finite field Fq of characteristic 2, thereby extending the algorithm of Kedlaya for ...