Liminf-results for sums with Kronecker sequence
Abstract
For irrational θ and 1-periodic function f we consider sums Σ0Q-1f(kθ+) where ∈ R. Sidorov proved that if f is absolutely continuous function, then Q ∞ |Σ0Q-1f(kθ+)| = 0 for any irrational θ and any ∈ R. The article shows that this property is not a criterion of absolute continuity, and also obtains some other results concerning the liminf-properties of these sums.
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