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.
| Original language | English |
|---|---|
| Journal | Journal of Integer Sequences |
| Volume | 8 |
| Issue number | 2 |
| Publication status | Published - 16 May 2005 |
Keywords
- Continued fraction expansion
- Elliptic curve
- Function field of characteristic zero
- Somos sequence
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Cite this
Van Der Poorten, A. J. (2005). Elliptic curves and continued fractions. Journal of Integer Sequences, 8(2).