The lower p-series of analytic pro-p groups and Hausdorff dimension - Heras, Iker de las; Klopsch, Benjamin; Thillaisundaram, Anitha (Journal of the London Mathematical Society, 2025)
Let (Formula presented.) be a (Formula presented.) -adic analytic pro- (Formula presented.) group of dimension (Formula presented.), with lower (Formula presented.) -series (Formula presented.). We produce an approximate series which descends regularly in strata and whose terms deviate from (Formula presented.) in a uniformly bounded way. This brings to light a new set of rational invariants (Formula presented.), canonically associated to (Formula presented.), such that (Formula presented.) and such that the Hausdorff dimensions (Formula presented.) of closed subgroups (Formula presented.) with respect to (Formula presented.) are confined to the set (Formula presented.) In particular, the Hausdorff spectrum (Formula presented.) is discrete and consists of at most (Formula presented.) rational numbers.