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Corrigendum: Elliptic Curves and Quadratic Recurrence Sequences

Corrigendum: Elliptic Curves and Quadratic Recurrence Sequences Abstract The statement of the numerical values κ and z0 on page 167 of [1, Section 3] contained an error. The values that were actually used were (to nine decimal places):   κ=2ω1−∫1∞(4t3−4t+1)−1/2dt=1.859185431,z0=2ω3+∫−1∞(4t3−4t+1)−1/2dt=0.204680500+1.225694691i, these being shifted, by the periods 2ω1 and 2ω3 respectively, compared with the values given in [1] (with ω1 = 1.496729323 and ω3 = 1.225694691i). With τ0 = τ1 and σ(z) denoting the sigma function σ(z; g2, g3) with invariants g2 = 4, g3 = −1 associated with the elliptic curve given by equation (3.2), these values of κ and z0 yield   σ(κ)=1.555836426,A=τ0σ(z0)=0.112724016−0.824911686i,B=σ(κ)σ(z0)τ1σ(z0+κ)τ0=0.215971963+0.616028193i and the latter three values all agree with those stated in the paper (apart from rounding down the last digit in the imaginary part of A). 2000 Mathematics Subject Classification 11B37 (primary), 33E05, 37J35 (secondary). © London Mathematical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

Corrigendum: Elliptic Curves and Quadratic Recurrence Sequences

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References (2)

Publisher
Oxford University Press
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609306018844
Publisher site
See Article on Publisher Site

Abstract

Abstract The statement of the numerical values κ and z0 on page 167 of [1, Section 3] contained an error. The values that were actually used were (to nine decimal places):   κ=2ω1−∫1∞(4t3−4t+1)−1/2dt=1.859185431,z0=2ω3+∫−1∞(4t3−4t+1)−1/2dt=0.204680500+1.225694691i, these being shifted, by the periods 2ω1 and 2ω3 respectively, compared with the values given in [1] (with ω1 = 1.496729323 and ω3 = 1.225694691i). With τ0 = τ1 and σ(z) denoting the sigma function σ(z; g2, g3) with invariants g2 = 4, g3 = −1 associated with the elliptic curve given by equation (3.2), these values of κ and z0 yield   σ(κ)=1.555836426,A=τ0σ(z0)=0.112724016−0.824911686i,B=σ(κ)σ(z0)τ1σ(z0+κ)τ0=0.215971963+0.616028193i and the latter three values all agree with those stated in the paper (apart from rounding down the last digit in the imaginary part of A). 2000 Mathematics Subject Classification 11B37 (primary), 33E05, 37J35 (secondary). © London Mathematical Society

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: Oct 1, 2006

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