Asymptotic valuations of sequences satisfying first order recurrences

Details Asymptotic valuations of sequences satisfying first order recurrences Asymptotic valuations of sequences satisfying first order recurrences

2007-09-14

arxiv.org/abs/0709.2289v1

Mathematics

Number Theory

10 pages, 3 figures

Scientific paper

Let t[n] be a sequence that satisfies a first order homogeneous recurrence
t[n] = Q[n]*t[n-1], where Q is a polynomial with integer coefficients. The
asymptotic behavior of the p-adic valuation of t[n] is described under the
assumption that all the roots of Q in Z/pZ have nonvanishing derivative.

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