92 citations · 502 across the 56 of their papers we have counts for
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Salem sets with no arithmetic progressions
Pablo Shmerkin
We construct Salem sets in of any dimension (including ) which do not contain any arithmetic progressions of length . Moreover, the sets can be taken…
dimensions and projections of random measures
Daniel Galicer, Santiago Saglietti, Pablo Shmerkin +1
We prove preservation of dimensions (for ) under all orthogonal projections for a class of random measures on the plane, which includes (deterministic) homogeneous…
Absolute continuity of complex Bernoulli convolutions
Pablo Shmerkin, Boris Solomyak
We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimensio…
Projections of self-similar and related fractals: a survey of recent developments
Pablo Shmerkin
In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond ge…