Interactive 2d and 3d graphs of $G_t(\lambda)$ and $g_t(\lambda)$

A supplement to the paper "Distribution of Angles to Lattice Points Seen from a Fast Moving Observer" by Jack Anderson, Florin P. Boca, Cristian Cobeli, and Alexandru Zaharescu. (https://arxiv.org/abs/2307.14656)

3d graph of $G_t(\lambda)$

Renders a 3d graph of $G_t(\lambda)$ for $2/3 < t < 4$ and $0 < \lambda < 5/2$ with different colours to resemble the different domains over which $G_t(\lambda)$ can be defined as a piece-wise function. You can drag the graph with your mouse to view it from different angles.

Click “Evaluate”.

2d graph of $G_t(\lambda)$

Renders a 2d graph of $G_t(\lambda)$ for a fixed $t$, with a graph of numerical data for $G^*_{t,J}(\lambda)$ superimposed on top. You can drag the sliders to choose $t$ anywhere in the range $[0.025, 3]$ (if $t < 2/3$ then $e^{-\lambda}$ will show instead of $G_t(\lambda)$), and $J$ anywhere in the range $[20,300]$. There is also a slider to translate the graph of $G^*_{t,J}(\lambda)$ up or down, which by default is set to translate up by 0.04 in order to distinguish it from $G_t(\lambda)$.

Click “Evaluate”.

3d graph of $g_t(\lambda)$

Renders a 3d graph of $g_t(\lambda)$ for $2/3 < t < 4$ and $0 < \lambda < 5/2$ with different colours to resemble the different domains over which $g_t(\lambda)$ can be defined as a piece-wise function. You can drag the graph with your mouse to view it from different angles.

Click “Evaluate”.

2d graph of $g_t(\lambda)$

Renders a 2d graph of $g_t(\lambda)$ for a fixed $t$. You can drag the slider to choose $t$ anywhere in the range $[0.67, 3]$.

Click “Evaluate”.