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arXiv · 1808.09719

Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics

Hakan Ayral·A. Muhammed Uludağ
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Abstract

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 involution sends algebraic numbers of degree at least three to transcendental values. We also deduce some theoretical results concerning the continued fraction statistics of the generic values of this involution and compare them with the experimental results.

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Hakan Ayral, A. Muhammed Uludağ. 2018-08-29. Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics. https://arxiv.org/abs/1808.09719

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