Elliptic Curves and Quadratic Recurrence Sequences
By Andrew N. W. Hone. 2005
79 citations recorded by the source corpus.
Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bb9c7754ac4babe801ada09449cadddb01330270
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Citations in the corpus
- Elliptic curves and related sequences (2003, methodology): “) A different approach to the same problem is taken by Andy Hone in [14].”
- Recurrence Relations for Elliptic Sequences: Every Somos 4 is a Somos k (2004, background): “Andy Hone [5] has recently published an elegant proof that general Somos 4 sequences are given by Weierstrass σ-functions; Hone’s arguments can also be readily adjusted to give the theorem that we prove here (as is shown in a communication by Hone to the Robbins forum).”
- Sigma function solution of the initial value problem for Somos 5 sequences (2005, unknown): “…the general term of the sequence in terms of the Weierstrass sigma function associated with the curve E, and then applying the addition formula (1.10) σ(z + κ) σ(z − κ) σ(z)2σ(κ)2 = ℘(κ) − ℘(z) or its immediate consequence, σ(c + d) σ(c − d) σ(a + b) σ(a − b) −σ(b + d) σ(b − d) σ(a + c) σ(a…”