TY - GEN
T1 - Periodic continued fractions in elliptic function fields
AU - van der Poorten, Alfred J.
AU - Tran, Xuan Chuong
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84958123768&partnerID=8YFLogxK
U2 - 10.1007/3-540-45455-1_31
DO - 10.1007/3-540-45455-1_31
M3 - Conference proceeding contribution
AN - SCOPUS:84958123768
SN - 3540438637
VL - 2369
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 390
EP - 404
BT - Algorithmic Number Theory - 5th International Symposium, ANTS-V Sydney, Australia, July 7-12, 2002 Proceedings
PB - Springer, Springer Nature
T2 - 5th International Algorithmic Number Theory Symposium, ANTS 2002
Y2 - 7 July 2002 through 12 July 2002
ER -