Geodesic
On the Lower Range of Perron's Modular Function
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 808-816

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The modular function Mwas introduced by Perron in (6). M(ξ) (for irrational ξ) is denned by the property that the inequality is satisfied by an infinity of relatively prime pairs (p, q)for positive d,but by at most a finite number of such pairs for negative d.We will write for the continued fraction expansion of ξ ∈ (0, 1) and for any finite collection y1,..., yk of positive integers we will write It is known (see 6) that Where 
Kinney, J. R.; Pitcher, T. S. On the Lower Range of Perron's Modular Function. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 808-816. doi: 10.4153/CJM-1969-090-1
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