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math.NT2022★ 1 cited
Quantizations of Continued Fractions
A. Muhammed Uludağ, Esra Ünal Yilmaz
We introduce a four-parameter deformation of continued fractions, which we call -deformation. We study some particular cases and compare them with the q-deformation of continu…
math.NT2018
The conumerator
A. Muhammed Uludağ, Buket Eren Gökmen
In this paper, we answer the question: "what is the qth Fibonacci number, where q is a positive rational?". The answer is the codenominator function, which is an integral-valued ma…
math.NT2018
Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics
Hakan Ayral, A. Muhammed Uludağ
We study the values of the recently introduced involution J (jimm) of the real line, which is equivariant with the action of the group PGL(2,Z). We test our conjecture that this in…