
05965343
j
2013e.00404
Bracher, M.
Hetz, S.
Levitt, B.
Ontiveros, M.
Sewell, A.
Generalized continued fractions in real quadratic fields and Pell's equations.
JP J. Algebra Number Theory Appl. 22, No. 2, 211223 (2011).
2011
Pushpa Publishing House, Allahabad, Uttar Pradesh, India
EN
F65
continued fractions
Rosen fractions
Pell's equation
units in real quadratic fields
Zbl 0056.30703
Zbl 0992.11034
http://www.pphmj.com/abstract/5945.htm
This is the result of a successful research experience for undergraduates (REU) project. The main result is the determination of the Rosen $\lambda$fraction [{\it D. Rosen}, Duke Math. J. 21, 549563 (1954; Zbl 0056.30703)] expansion of all units of the ring of integers of $\mathbb Q(\lambda)$ when $\lambda = \sqrt{d}$ with $d>0$ squarefree, thus generalizing a result of {\it D. Rosen} and {\it C. Towse} [ Arch. Math. 77, No. 4, 294302 (2001; Zbl 0992.11034)].
Thomas Schmidt (Corvallis)