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Authors
Affiliations
1 Mathematics Department, Box 1917, Brown University, Providence, RI 02912, US
2 Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, GB
Source
Journal of the Ramanujan Mathematical Society, Vol 21, No 1 (2006), Pagination: 1-17
Abstract
An elliptic divisibility sequence (EDS) is a sequence of integers (Wn)n≥0 generated by the nonlinear recursion satisfied by the division polyomials of an elliptic curve. We give a formula for the sign of Wn for unbounded nonsingular EDS, a typical case being Sign (Wn)=(-1) └nβ┘ for an irrational number β∈ℝ. As an application, we show that the associated sequence of absolute values (|Wn|) cannot be realized as the fixed point counting sequence of any abstract dynamical system.