Multiplicities of Linear Recurrence Sequences
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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.
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Patrick Allen (2006). Multiplicities of Linear Recurrence Sequences. UWSpace. http://hdl.handle.net/10012/2942