id: 05965343
dt: j
an: 2013e.00404
au: Bracher, M.; Hetz, S.; Levitt, B.; Ontiveros, M.; Sewell, A.
ti: Generalized continued fractions in real quadratic fields and Pell’s
equations.
so: JP J. Algebra Number Theory Appl. 22, No. 2, 211-223 (2011).
py: 2011
pu: Pushpa Publishing House, Allahabad, Uttar Pradesh, India
la: EN
cc: F65
ut: continued fractions; Rosen fractions; Pell’s equation; units in real
quadratic fields
ci: Zbl 0056.30703; Zbl 0992.11034
li: http://www.pphmj.com/abstract/5945.htm
ab: This is the result of a successful research experience for undergraduates
(REU) project. The main result is the determination of the Rosen
$λ$-fraction [{\it D. Rosen}, Duke Math. J. 21, 549‒563 (1954; Zbl
0056.30703)] expansion of all units of the ring of integers of $\mathbb
Q(λ)$ when $λ= \sqrt{d}$ with $d>0$ square-free, thus generalizing a
result of {\it D. Rosen} and {\it C. Towse} [ Arch. Math. 77, No. 4,
294‒302 (2001; Zbl 0992.11034)].
rv: Thomas Schmidt (Corvallis)