Geodesic
Elliptic curves and continued fractions
Journal of integer sequences, Tome 8 (2005) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 11A55, 11G05, 14H05, 14H52
Keywords: continued fraction expansion, function field of characteristic zero, elliptic curve, somos sequence 
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     author = {van der Poorten, Alfred J.},
     title = {Elliptic curves and continued fractions},
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     language = {en},
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van der Poorten, Alfred J. Elliptic curves and continued fractions. Journal of integer sequences, Tome 8 (2005) no. 2. http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a0/