Computing zeta functions of algebraic curves using Harvey’s trace formula-Reference-Cited by-同舟云学术

Computing zeta functions of algebraic curves using Harvey’s trace formula

Published:2022-11-10 Issue:4 Volume:8 Page:
ISSN:2522-0160
Container-title:Research in Number Theory
language:en
Short-container-title:Res. number theory

Author:

Kyng Madeleine^ORCID

Abstract

AbstractWe present a new method for computing the zeta function of an algebraic curve over a finite field. The algorithm relies on a trace formula of Harvey to count points on a plane model of the curve. The zeta function of the curve is then obtained by making corrections at singular points. We report on an implementation and provide some examples in MAGMA which demonstrate an improvement over Tuitman’s algorithm.

Funder

University of New South Wales

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory

Link

https://link.springer.com/content/pdf/10.1007/s40993-022-00398-7.pdf

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