In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and a result due to Brindza, Pintér and Schmidt. We then investigate ternary recurrences and exhibit a result due to Beukers building on work of Beukers and Tijdeman. The last two chapters deal with a very important result due to Schmidt in which we bound the zero-multiplicity of a linear recurrence sequence of order <em>t</em> by a function involving <em>t</em> alone. Moreover we improve on Schmidt's bound by making some minor changes to his argument.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/2942 |
| Date | January 2006 |
| Creators | Allen, Patrick |
| Publisher | University of Waterloo |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | application/pdf, 559709 bytes, application/pdf |
| Rights | Copyright: 2006, Allen, Patrick. All rights reserved. |
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