0-Multiplicity of Ternary Rational Linear Sequences

eBook (PDF), 118 Pages
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The 20th century saw a large number of results regarding the Zero-multiplicity of rational linear recurrence sequences; those are the number of times zero is found in a particular recurrence sequence. Of particular interest is the result of Skolem-Mahler-Lech and the result of F. Beukers. Respectively these results are: for every linear recurrence sequence the zeroes are a finite set along with a finite number of arithmetic sequences, and, with the exception of a special subset, every ternary linear recurrence sequence has a multiplicity less than seven. Both of these results rely heavily on p-adic techniques and the behavior of algebraic numbers within the p-adic numbers.
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October 2, 2011
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