De Koninck, Jean-Marie; Kátai, Imre Some new methods for constructing normal numbers. (English) Zbl 1295.11081 Ann. Sci. Math. Qué. 36, No. 2, 349-359 (2012). Summary: Given an integer \(q \leq 2\), a \(q\)-normal number is a real number whose \(q\)-ary expansion is such that any preassigned sequence of length \(k \leq 1\), of base \(q\) digits from this expansion, occurs at the expected frequency, namely \(1/q^k\). We expose two new methods which allow the construction of large families of \(q\)-normal numbers. Cited in 1 ReviewCited in 3 Documents MSC: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. Keywords:\(q\)-normal number; \(q\)-ary expansion; \(q\)-ary smooth sequence PDFBibTeX XMLCite \textit{J.-M. De Koninck} and \textit{I. Kátai}, Ann. Sci. Math. Qué. 36, No. 2, 349--359 (2012; Zbl 1295.11081)