Zeros and completeness for vertically stretched Ford circles

Determine whether each suitably vertically stretched Ford circle contains exactly n zeros of G_{\{2\}^n} and whether G_{\{2\}^n} has no other zeros.

Background

The paper studies the distribution of zeros of G_{{2}^n} relative to Ford circles. Numerical experiments indicate that the usual Ford circles are too small for n≥3, because some zeros lie above the height of the corresponding ordinary Ford circle.

The authors propose vertically stretching the Ford circles and conjecture that the stretched regions capture precisely n zeros of G_{{2}^n}, with no additional zeros elsewhere. The paper proves only the special case n=2, showing that each ordinary Ford circle contains exactly two distinct simple zeros of G_{2,2}.