Computing zeta functions of Artin-Schreier curves over finite fields II

Journal article

We describe a method which may be used to compute the zeta function of an arbitrary Artin-Schreier cover of the projective line over a finite field. Specifically, for covers defined by equations of the form Z^p - Z = f (X) we present, and give the complexity analysis of, an algorithm for the case in which f (X) is a rational function whose poles all have order 1. However, we only prove the correctness of this algorithm when the field characteristic is at least 5. The algorithm is based upon a cohomological formula for the L-function of an additive character sum. One consequence is a practical method of finding the order of the group of rational points on the Jacobian of a hyperelliptic curve in characteristic 2. © 2003 Elsevier Inc. All rights reserved.

Authors: Lauder, A; Wan, D; Wan, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Complexity
• Volume: 20
• Issue: 2-3
• Pages: 331-349
• Publication date: 2004-04-01
• ISSN: 0885-064X
• Keywords: Artin-Schreier curve; Hyperelliptic curve; Zeta function; Algorithm; Finite field
• Subjects: Mathematics