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Algebraic divisibility sequences over function fields
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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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Official URL: http://dx.doi.org/10.1017/S1446788712000092
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 | ||||
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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: |
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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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