Periodic continued fractions in elliptic function fields

Alfred J. van der Poorten, Xuan Chuong Tran

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

10 Citations (Scopus)


We construct all families of quartic polynomials over Q whose square root has a periodic continued fraction expansion, and detailthose expansions. In particular we prove that, contrary to expectation, the cases of period length nine and eleven do not occur. We conclude by providing a list of examples of pseudo-elliptic integrals involving square roots of polynomials of degree four. The primary issue is of course the existence of units in elliptic function fields over Q. That, and related issues are surveyed in the paper’s introduction.

Original languageEnglish
Title of host publicationAlgorithmic Number Theory - 5th International Symposium, ANTS-V Sydney, Australia, July 7-12, 2002 Proceedings
PublisherSpringer, Springer Nature
Number of pages15
ISBN (Print)3540438637
Publication statusPublished - 2002
Event5th International Algorithmic Number Theory Symposium, ANTS 2002 - Sydney, Australia
Duration: 7 Jul 200212 Jul 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)03029743
ISSN (Electronic)16113349


Other5th International Algorithmic Number Theory Symposium, ANTS 2002


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