ICC   25427
INSTITUTO DE INVESTIGACION EN CIENCIAS DE LA COMPUTACION
Unidad Ejecutora - UE
artículos
Título:
On the construction of absolutely normal numbers
Autor/es:
THEODORE SLAMAN; CHRISTOPH C. AISTLEITNER; VERĂ“NICA BECHER; ADRIAN-MARIA SCHEERER
Revista:
ACTA ARITHMETICA
Editorial:
POLISH ACAD SCIENCES INST MATHEMATICS
Referencias:
Lugar: VARSOVIA; Año: 2017 vol. 180 p. 333 - 346
ISSN:
0065-1036
Resumen:
We give a construction of an absolutely normal real number x such that for every integer b greater than or equal to 2, the discrepancy of the first N terms of the sequence (bnx mod 1)n≥0 is of asymptotic order O(N−1/2). This is below the order of discrepancy which holds for almost all real numbers. Even the existence of absolutely normal numbers having a discrepancy of such a small asymptotic order was not known before.