Multiplicities of Linear Recurrence Sequences

[摘要] 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 t by a function involving t alone.Moreover we improve on Schmidt;;s bound by making some minor changes to his argument.

[发布机构] University of Waterloo

[效力级别] linear recurrence

[关键词] Mathematics;linear recurrence;diophantine equations;number theory