Elliptic curves and continued fractions

Details Elliptic curves and continued fractions Elliptic curves and continued fractions

2004-03-14

arxiv.org/abs/math/0403225v3

Mathematics

Number Theory

v1; final -- I hope

Scientific paper

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.

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