Computing Zeta Functions of Superelliptic Curves in Larger Characteristic

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 characteristic p to the superelliptic case. As result we obtain the most general Kedlaya-style point-counting algorithm that runs soft linear in p1/2 . Mathematics Subject Classification (2000). Primary 14Q05; Secondary 11M38. Keywords. Zeta functions, Kedlaya’s Algorithm, Superelliptic Curves.

• Type: Journal
• Year: 2010
• Where: MICS
• Authors: Moritz Minzlaff
• Keywords: Algorithm, Kedlaya-style Point-counting Algorithm, Mathematics Subject Classification, MICS 2010