Mahler, Kurt

Reprint: Über die Dezimalbruchentwicklung gewisser Irrationalzahlen (1937)

Doc. Math. Extra Vol. Mahler Selecta, 459-474 (2019)
DOI: 10.25537/dm.2019.SB-459-474


Let \((n)_q\) denote the base-\(q\) expansion of the integer \(n\). The Champernowne number to the base \(q\) is the concatenation of the base-\(q\) expansions of the positive integers after a radix point; that is, the number \[0.(1)_q(2)_q(3)_q\cdots(n)_q\cdots. \] In this paper, Mahler shows that each of these numbers is transcendental, but is not a Liouville number. \par Reprint of the author's paper [Mathematica B, Zutphen 6, 22--36 (1937; Zbl 0018.11102; JFM 63.0155.03)].

Mathematics Subject Classification

11-03, 11J81, 11J91