Elliptic curves and continued fractions

Alfred J. Van Der Poorten

Elliptic curves and continued fractions

Alfred J. Van Der Poorten^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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

Cite this

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title = "Elliptic curves and continued fractions",

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AU - Van Der Poorten, Alfred J.

PY - 2005/5/16

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N2 - 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.

AB - 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.

KW - Continued fraction expansion

KW - Elliptic curve

KW - Function field of characteristic zero

KW - Somos sequence

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M3 - Article

AN - SCOPUS:21244470724

VL - 8

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

SN - 1530-7638

IS - 2

ER -

Elliptic curves and continued fractions

Abstract

Keywords

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