Elliptic Curves and Continued Fractions

  title={Elliptic Curves and Continued Fractions},
  author={Alfred J. van der Poorten},
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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Memoir on elliptic divisibility sequences, Amer

  • Morgan Ward
  • J. Math
  • 1948
Highly Influential
5 Excerpts

The strange and surprising saga of the Somos sequences

  • David Gale
  • Mathematical Intelligencer
  • 1991
Highly Influential
3 Excerpts

Periodic continued fractions and elliptic curves, in High Primes and Misdemeanours : lectures in honour of the 60th birthday

  • Alfred J. van der Poorten
  • Fields Institute Communications
  • 2004
2 Excerpts

Memoir on elliptic divisibility sequences

  • Morgan Ward
  • Elliptic curves and related sequences , PhD…
  • 2003

On continued fractions and diophantine approximation in power series fields

  • M Wolfgang, Schmidt
  • Acta Arith
  • 2000
2 Excerpts

Quasi-elliptic integrals and periodic continued fractions

  • Alfred J. van der Poorten, Xuan Chuong Tran
  • Monatshefte Math.,
  • 2000

van der Poorten and Xuan Chuong Tran , Quasi - elliptic integrals and periodic continued fractions

  • J Alfred
  • Monatshefte Math .
  • 2000

talk at “The Mathematics of Public Key Cryptography”, Toronto 1999; see http://homepages.gold.ac.uk/rachel/toronto/sld006.htm

  • Rachel Shipsey
  • 1999

On periodicity of continued fractions in hyperelliptic function fields

  • T. G. Berry
  • Arch. Math
  • 1990
2 Excerpts

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