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

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

ER -