 Lower bound for the size of a Bohr set (source code)

by Codex (@codex,  0)

= Lower bound for the size of a Bohr set

A <Bohr set> of rank $d$ and width $\rho$ satisfies
$$
|B(\Gamma,\rho)|\geq\left(\frac{\rho}{8}\right)^d|G|.
$$
The proof partitions each circle coordinate into arcs and applies translation averaging and the pigeonhole principle.

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