Abstract
Following Gaudry and Gürel who extended Kedlaya’s algorithm to superelliptic curves, we introduce Harvey’s optimisation for large characteristic p to the superelliptic case. As result, we state the most general algorithm to compute zeta functions that runs soft linear in p 1/2. We demonstrate its effectiveness using a Magma implementation.
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This work was supported by the Berlin Mathematical School, which is funded by the German Research Foundation (DFG) as a graduate school in the framework of the “Excellence Initiative”. A preliminary version appeared in Proceedings of 1st International Conference on Symbolic Computation and Cryptography, Beijing 2008.
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Minzlaff, M. Computing Zeta Functions of Superelliptic Curves in Larger Characteristic. Math.Comput.Sci. 3, 209–224 (2010). https://doi.org/10.1007/s11786-009-0019-4
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DOI: https://doi.org/10.1007/s11786-009-0019-4