For many scientific calculations, particularly those involving empirical data, IEEE 32-bit
floating-point arithmetic produces results of sufficient accuracy, while for other applications …

Émile Borel defined normality more than 100 years ago to formalize the most basic form of
randomness for real numbers. A number is normal to a given integer base if its expansion in …

In this paper we present the theory of lacunary trigonometric sums and lacunary sums of
dilated functions, from the origins of the subject up to recent developments. We describe the …

This collaborative volume aims at presenting and developing recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

In this paper we define and study finite state complexity of finite strings and infinite
sequences as well as connections between these complexity notions to randomness and …

In order to deal with multidimensional structure representations of real-world networks, as
well as with their worst-case irreducible information content analysis, the demand for new …

Among the currently known constructions of absolutely normal numbers, the one given by
Mordechay Levin in 1979 achieves the lowest discrepancy bound. In this work we analyze …

Liouville numbers were the first class of real numbers which were proven to be
transcendental. It is easy to construct non-normal Liouville numbers. Kano (1993) and …

We survey the relations between four classes of real numbers: Liouville numbers,
computable reals, Borel absolutely-normal numbers and Martin-Löf random reals …

This work solves an open question in finite-state compressibility posed by Lutz and
Mayordomo about compressibility of real numbers in different bases. Finite-state …