6 citations · 6 across the 7 of their papers we have counts for
9 papers
Equivariant Modular Functions and Quantizations of Continued Fractions
Mustafa Topkara, A. Muhammed Uludag
We show that, in addition to the quantizations of the rational numbers discovered by Morier-Genoud and Ovsienko, there exist a pair of conjugate representations of the modular grou…
Composition laws on the Fricke surface and Markov triples
A. Muhammed Uludağ, Esra Ünal Yılmaz
We determine some composition laws related to the Fricke surface and the "double" Fricke surface. This latter surface admits the squares of Markov triples as its solutions.
InfoMod: A visual and computational approach to Gauss' binary quadratic forms
Ayberk Zeytin, Hakan Ayral, A. Muhammed Uludağ
InfoMod is a new software and application devoted to the modular group, PSL2(Z). It has algorithms that deals with the classical correspondences among continued fractions, geodesic…
A panaroma of the fundamental group of the modular orbifold
A. Muhammed Uludağ, Ayberk Zeytin
We give an overview of the category of subgroups of the modular group, incorporating both the tame part, i.e. finite index subgroups, and the non-tame part, i.e. the rest. We also…
Binary quadratic forms as dessins
A. Muhammed Uludağ, Ayberk Zeytin, Merve Durmuş
We show that the class of every primitive indefinite binary quadratic form is naturally represented by an infinite graph (named çark) with a unique cycle embedded on a conformal an…
Jimm, a Fundamental Involution
A. Muhammed Uludağ, Hakan Ayral
We study the involution of the real line induced by the outer automorphism of the extended modular group PGL(2,Z). This `modular' involution is discontinuous at rationals but satis…