Vol. 4, No. 5, 2010

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
The Manin constant of elliptic curves over function fields

Ambrus Pál

Vol. 4 (2010), No. 5, 509–545
Abstract

We study the p-adic valuation of the values of normalised Hecke eigenforms attached to nonisotrivial elliptic curves defined over function fields of transcendence degree one over finite fields of characteristic p. We derive upper bounds on the smallest attained valuation in terms of the minimal discriminant under a certain assumption on the function field, and provide examples to show that our estimates are optimal. As an application of our results, we prove the analogue of the degree conjecture unconditionally for strong Weil curves with square-free conductor defined over function fields satisfying the assumption mentioned above.

Keywords
elliptic curves, Hecke eigenforms, degree conjecture
Mathematical Subject Classification 2000
Primary: 11G05
Secondary: 11G40, 14F30
Milestones
Received: 31 March 2009
Revised: 2 December 2009
Accepted: 31 December 2009
Published: 10 July 2010
Authors
Ambrus Pál
Department of Mathematics
Imperial College
180 Queen’s Gate
London, SW7 2AZ
United Kingdom