Abstract
I detail the continued fraction expansion of the square root of a monic polynomials of even degree. In the quartic and sextic cases I observe explicitly that parameters appearing in the continued fraction expansion yield integer sequences defined by relations instancing sequences of Somos type. Because each step in the expansion corresponds to addition by the divisor at infinity on (the Jacobian of) the relevant curve I recover the link between Somos sequences and the $mathrm{c}$ -ordinates of the multiples of a point on certain curves.
Original language | English |
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Pages (from-to) | 98-107 |
Number of pages | 10 |
Journal | Proceedings of the RIMS symposium “Analytic Number Theory and Surrounding Areas” |
Publication status | Published - 2006 |
Event | Analytic Number Theory and Surrounding Areas - Kyoto Duration: 18 Oct 2004 → 22 Oct 2004 |
Keywords
- continued fraction expansion
- function field of characteristic zero
- hyperelliptic curve
- Somos sequence