Far Eastern Mathematical Journal

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A simplified proof of Ward's formula for elliptic sequences


Ustinov A.V.

2019, issue 1, . 84-87


Abstract
An elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials on elliptic curves. EDS were first defined, and their arithmetic properties studied, by Morgan Ward in the 1948. In particular he has proven an explicit formula for the general term of the sequence in terms of the Weierstrass sigma function. In the present paper we give a simplified proof of Ward's formula.

Keywords:
elliptic divisibility sequence, elliptic curves, Weierstrass elliptic functions

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References

[1] M. Ward, Memoir on elliptic divisibility sequences, Amer. J. Math., 70, (1948), 3174.
[2] Abramowitz, Milton, and Irene A. Stegun., Handbook of mathematical functions: with for-mulas, graphs, and mathematical tables, v. 55, Courier Corporation, 1965.

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