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:

    “The windy springs and the blazing summers, one after another, had enriched and mellowed that flat tableland; all the human effort that had gone into it was coming back in long, sweeping lines of fertility. The changes seemed beautiful and harmonious to me; it was like watching the growth of a great man or of a great idea. I recognized every tree and sandbank and rugged draw. I found that I remembered the conformation of the land as one remembers the modelling of human faces.”
    —Willa Cather (1873–1947)

    “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)