Ingram, Patrick, Mahe, Valery, Silverman, Joseph H., Stange, Katherine E. and Streng, Marco (2012) Algebraic divisibility sequences over function fields. Journal of the Australian Mathematical Society, Volume 92 (Number 01). pp. 99-126. doi:10.1017/S1446788712000092 ISSN 1446-7887.

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Abstract

In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Curves, Algebraic , Curves, Elliptic
Journal or Publication Title:	Journal of the Australian Mathematical Society
Publisher:	Cambridge University Press
ISSN:	1446-7887
Official Date:	February 2012
Dates:	Date Event February 2012 Published
Volume:	Volume 92
Number:	Number 01
Page Range:	pp. 99-126
DOI:	10.1017/S1446788712000092
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	25 December 2015
Date of first compliant Open Access:	25 December 2015
Funder:	Natural Sciences and Engineering Research Council of Canada (NSERC) , Université de Franche-Comté, National Science Foundation (U.S.) (NSF), Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	DMS-0854755, MSPRF 0802915 (NSF) ; PDF-373333 (NSERC) ; EP/G004870/1 (EPSRC)

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