Ergodic group automorphisms are exponentially recurrent

We show that ergodic automorphisms of compact abelian groups have the property that for every nonempty open setU, the measure of the set first returning toU aftern iterates decays exponentially inn. This follows from a result about aperiodic automorphisms of countable abelian groups, whose proof employsp-adic analysis. Partially supported by NSF Grant MCS 7704915.