Abstract
Riesz products on the ring of p-adic integers are introduced and studied from the points of view of harmonic analysis and dynamical system relative to the shift transformation. We find necessary and sufficient conditions for a Riesz product to be invariant, quasi-invariant or quasi-Bernoulli. We study the mutual absolute continuity of two Riesz products and the almost everywhere convergence of lacunary series with respect to a Riesz product. We also compute the Hausdorff dimension and the energy dimension and prove a multifractal formalism for a given Riesz product.
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