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math.NT2013
Arithmetic Differential Equations of Painleve' VI Type
Alexandru Buium, Yuri I. Manin
Using the description of Paileve' VI family of differential equations in terms of a universal elliptic curve, going back to R. Fuchs (cf. [Ma96]), we translate it into the realm of…
math.NT2001★ 5 cited
Continued fractions, modular symbols, and non-commutative geometry
Yuri I. Manin, Matilde Marcolli
Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one t…