Divisibility Sequence
نویسنده
چکیده
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.
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تاریخ انتشار 2004