Geodesic
Cyclic products of purely periodic irrationals
Journal of integer sequences, Tome 17 (2014) no. 4
Zbl
Let $\left(a_{0}, \dotsb ,a_{k-1} \right)$ be a sequence of positive integers and $m$ a positive integer. We prove that "almost every" real quadratic unit $\epsilon$ of norm (-1)$^{k}$ admits at least $m$ distinct factorizations into a product of purely periodic irrationals of the form
Classification : 11A55, 11N32, 37D20
Keywords: simple continued fraction, purely periodic irrational, prime represented by quadratic polynomial, linear automorphism of the torus, Anosov automorphism 
Carroll,  C.R. Cyclic products of purely periodic irrationals. Journal of integer sequences, Tome 17 (2014) no. 4. http://geodesic.mathdoc.fr/item/JIS_2014__17_4_a2/
@article{JIS_2014__17_4_a2,
     author = {Carroll,  C.R.},
     title = {Cyclic products of purely periodic irrationals},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {4},
     zbl = {1360.11017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_4_a2/}
}
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