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Asymptotic valuations of sequences satisfying first order recurrences

Author(s): Tewodros Amdeberhan; Luis A. Medina; Victor H. Moll
Journal: Proc. Amer. Math. Soc. 137 (2009), 885-890.
MSC (2000): Primary 11B37; Secondary 11B50, 11B83
Posted: September 24, 2008
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Abstract: 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. We describe the asymptotic behavior of the $ p$-adic valuation of $ t_n$.

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F. Gouvea.
$ p$-adic Numbers.
Springer-Verlag, 2nd edition, 1997. MR 1488696 (98h:11155)

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S. Lang.
Algebra.
Springer-Verlag, revised third edition, 2002. MR 1878556 (2003e:00003)

3.
M. Ram Murty.
Introduction to $ p$-adic Analytic Number Theory, volume 27 of Studies in Advanced Mathematics.
American Mathematical Society, 1st edition, 2002. MR 1913413 (2003c:11151)

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Additional Information:

Tewodros Amdeberhan
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: tamdeberhan@math.tulane.edu

Luis A. Medina
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: lmedina@math.tulane.edu

Victor H. Moll
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: vhm@math.tulane.edu

DOI: 10.1090/S0002-9939-08-09580-4
PII: S 0002-9939(08)09580-4
Keywords: Valuations, Hensel's lemma, recurrences
Received by editor(s): September 10, 2007,
Received by editor(s) in revised form: March 18, 2008
Posted: September 24, 2008
Communicated by: Martin Lorenz
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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