On uniformly distributed sequences of integers and Poincaré recurrence
The author proves that Hartmann-uniformly distributed sequences are sequences of strong Poincaré recurrence. Theorems 1, 2 in fact follow (from equality instead of the stated inequality) already from the much more general fact, that Hartmann-uniformly distributed sequences are uniformly distributed with respect to any unitary representation (even with respect to the strong operator topology) not only for locally compact abelian groups, as considered here (or groups with only finite-dimensional irreducible representations, considering a natural generalization), see [\textit{J. Blum} and \textit{B. Eisenberg}, Proc. Am. Math. Soc. 42, 423-429 (1974; Zbl 0273.43004) and \textit{H. Rindler}, Monatsh. Math. 82, 207-235 (1976; Zbl 0361.43002), p. 209, Def. 4 and the following remark]. The explicit examples given in Theorem 4 are interesting, but most of them are well-known. For Part II see Zbl 0922.11065.
Hartmann-uniformly distributed sequences
scientific article; zbMATH DE number 1251251