Periods of quadratic irrationalities, and torsion of elliptic curves
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V. A. Malyshev
Translated by: the author - St. Petersburg Math. J. 15 (2004), 587-602
- DOI: https://doi.org/10.1090/S1061-0022-04-00824-6
- Published electronically: July 7, 2004
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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
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- V. A. Malyshev, The Abel equation, Algebra i Analiz 13 (2001), no. 6, 1–55 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 13 (2002), no. 6, 893–938. MR 1883839
Bibliographic Information
- V. A. Malyshev
- Affiliation: Rybinsk State Aviation Technology Academy, Rybinsk, Russia
- Email: wmal@ryb.adm.yar.ru
- Received by editor(s): March 10, 2003
- Published electronically: July 7, 2004
- © Copyright 2004 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 587-602
- MSC (2000): Primary 14K20, 11A55
- DOI: https://doi.org/10.1090/S1061-0022-04-00824-6
- MathSciNet review: 2068984