Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.5

Elliptic Curves and Continued Fractions

Alfred J. van der Poorten
Centre for Number Theory Research
1 Bimbil Place
Killara, Sydney NSW 2071
Australia

Abstract: We detail the continued fraction expansion of the square root of the general monic quartic polynomial, noting that each line of the expansion corresponds to addition of the divisor at infinity. We analyse the data yielded by the general expansion. In that way we obtain "elliptic sequences" satisfying Somos relations. I mention several new results on such sequences. The paper includes a detailed "reminder exposition" on continued fractions of quadratic irrationals in function fields.

(Concerned with sequences A006720 and A006721 .)

Received September 20 2004; revised version received November 18 2004. Published in Journal of Integer Sequences May 16 2005.