Vol. 314, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 315: 1  2
Vol. 314: 1  2
Vol. 313: 1  2
Vol. 312: 1  2
Vol. 311: 1  2
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Recovering affine curves over finite fields from $L$-functions

Jeremy Booher and José Felipe Voloch

Vol. 314 (2021), No. 1, 1–28
Abstract

Let C be an algebraic curve over a finite field of odd characteristic. We investigate using L-functions of Galois extensions of the function field K of C to effectively recover the curve C. When C is the projective line with four rational points removed, we show how to use L-functions of a ray class field of K to effectively recover the removed points up to automorphisms of the projective line. When C is a plane curve, we show how to effectively recover the equation of C using L-functions of Artin–Schreier covers.

PDF Access Denied

We have not been able to recognize your IP address 54.224.133.198 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
L-functions, function fields, curves, finite fields, recovering function fields, ray class field, Artin–Schreier cover
Mathematical Subject Classification
Primary: 11G20
Milestones
Received: 18 February 2021
Revised: 5 July 2021
Accepted: 11 July 2021
Published: 15 October 2021
Authors
Jeremy Booher
School of Mathematics and Statistics
University of Canterbury
Christchurch
New Zealand
José Felipe Voloch
School of Mathematics and Statistics
University of Canterbury
Christchurch
New Zealand