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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Periods of quadratic irrationalities, and torsion of elliptic curves

Author: V. A. Malyshev
Translated by: the author
Original publication: Algebra i Analiz, tom 15 (2003), nomer 4.
Journal: St. Petersburg Math. J. 15 (2004), 587-602
MSC (2000): Primary 14K20, 11A55
Published electronically: July 7, 2004
MathSciNet review: 2068984
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Abstract | References | Similar Articles | Additional Information

Abstract: For rational $A$, $B$, $C$, $D$, the period length for the continued fraction of the square root \[ {\sqrt {t^{4}+At^{3}+Bt^{2}+Ct+D}}\] can only take the values $1$, $2$, $3$, $4$, $5$, $6$, $8$, $10$, $14$, $18$, $22$, and perhaps $9$ and $11$.

References [Enhancements On Off] (What's this?)

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Additional Information

V. A. Malyshev
Affiliation: Rybinsk State Aviation Technology Academy, Rybinsk, Russia

Keywords: Quadratic irrationalities, elliptic curves
Received by editor(s): March 10, 2003
Published electronically: July 7, 2004
Article copyright: © Copyright 2004 American Mathematical Society