Valuations of Somos 4 sequences and canonical local heights on elliptic curves-Reference-Cited by-同舟云学术

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

Published:2011-01-12 Issue:3 Volume:150 Page:385-397
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

UCHIDA YUKIHIRO

Abstract

AbstractSomos 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference21 articles.

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