Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics
Number Theory
2018-08-30 v1
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.
Keywords
Cite
@article{arxiv.1808.09719,
title = {Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics},
author = {Hakan Ayral and A. Muhammed Uludağ},
journal= {arXiv preprint arXiv:1808.09719},
year = {2018}
}
Comments
23 pages, 5 figures, 6 tables