Mathematics – Number Theory
Scientific paper
2005-01-11
Mathematics
Number Theory
Typos corrected in sections 2,3,4,5. To appear in Journal of Nonlinear Mathematical Physics for proceedings of SIDE 6, Helsink
Scientific paper
The Somos 4 sequences are a family of sequences satisfying a fourth order bilinear recurrence relation. In recent work, one of us has proved that the general term in such sequences can be expressed in terms of the Weierstrass sigma function for an associated elliptic curve. Here we derive the analogous family of sequences associated with an hyperelliptic curve of genus two defined by the affine model $y^2=4x^5+c_4 x^4+ ... +c_1 x+c_0$. We show that the recurrence sequences associated with such curves satisfy bilinear recurrences of order 8. The proof requires an addition formula which involves the genus two Kleinian sigma function with its argument shifted by the Abelian image of the reduced divisor of a single point on the curve. The genus two recurrences are related to a B\"{a}cklund transformation (BT) for an integrable Hamiltonian system, namely the discrete case (ii) H\'{e}non-Heiles system.
Braden Harry W.
Enolskii Victor Z.
Hone Andrew N. W.
No associations
LandOfFree
Bilinear recurrences and addition formulae for hyperelliptic sigma functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bilinear recurrences and addition formulae for hyperelliptic sigma functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bilinear recurrences and addition formulae for hyperelliptic sigma functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-201960