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Valuations of Somos 4 sequences and canonical local heights on elliptic curves

Published online by Cambridge University Press:  12 January 2011

YUKIHIRO UCHIDA
YUKIHIRO UCHIDA*
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan. e-mail: uchida@math.kyoto-u.ac.jp
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Abstract

Somos 4 sequences are sequences of numbers defined by a bilinear recurrence relation of order 4 and include elliptic divisibility sequences as a special case. In this paper, we describe valuations of Somos 4 sequences in terms of canonical local heights on the associated elliptic curves. We consider both Archimedean and non-Archimedean valuations. As applications, we study the asymptotic behaviour of valuations of Somos 4 sequences and obtain another proof of the integrality of certain Somos 4 sequences.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 3 , May 2011 , pp. 385 - 397
Copyright
Copyright © Cambridge Philosophical Society 2011

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