Elliptic Divisibility Sequence - Growth of EDS

Growth of EDS

Let (Wn)n ≥ 1 be a nonsingular EDS that is not periodic. Then the sequence grows quadratic exponentially in the sense that there is a positive constant h such that

\lim_{n\to\infty} \frac{\log |W_n|}{n^2} = h > 0.

The number h is the canonical height of the point on the elliptic curve associated to the EDS.

Read more about this topic:  Elliptic Divisibility Sequence

Famous quotes containing the words growth of and/or growth:

    “Next to the right of liberty, the right of property is the most important individual right guaranteed by the Constitution and the one which, united with that of personal liberty, has contributed more to the growth of civilization than any other institution established by the human race.”
    —William Howard Taft (1857–1930)

    “The risk for a woman who considers her helpless children her “job” is that the children’s growth toward self-sufficiency may be experienced as a refutation of the mother’s indispensability, and she may unconsciously sabotage their growth as a result.”
    —Letty Cottin Pogrebin (20th century)