Robert Hines

activity

20172020

most citedAn infinite product on the Teichmüller space of the once-punctured torus

1 citations · 1 across the 2 of their papers we have counts for

collaborators

4 papers

math.GT2020★ 1 cited

An infinite product on the Teichmüller space of the once-punctured torus

Robert Hines

We prove the identity $γ \prod (\frac{e ^{l (γ)} + 1}{e ^{l (γ)} - 1})^{2 h} = exp (\frac{l _{1} + l _{2} + l _{3}}{2}),$ (or $$ \prod_γ\left(\frac{t(γ)^2}{t(γ)^2-4}\right)^h=\fra…

math.NT2018

Examples of badly approximable vectors over number fields

Robert Hines

We consider approximation of vectors $z \in F \otimes R ≅ R^{r} \times C^{s}$ by elements of a number field $F$ and construct examples of badly approxi…

math.NT2017

Badly approximable numbers over imaginary quadratic fields

Robert Hines

We recall the notion of nearest integer continued fractions over the Euclidean imaginary quadratic fields $K$ and characterize the "badly approximable" numbers, ( $z$ such that ther…

math.NT2017

The Dynamics of Super-Apollonian Continued Fractions

Sneha Chaubey, Elena Fuchs, Robert Hines +1

We examine a pair of dynamical systems on the plane induced by a pair of spanning trees in the Cayley graph of the Super-Apollonian group of Graham, Lagarias, Mallows, Wilks and Ya…