Artículos de revistas
On the construction of absolutely normal numbers
Fecha
2017-12Registro en:
Aistleitner, Christoph; Becher, Veronica Andrea; Scheerer, Adrian-Maria; Slaman, Theodore A.; On the construction of absolutely normal numbers; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 180; 4; 12-2017; 333-346
0065-1036
CONICET Digital
CONICET
Autor
Aistleitner, Christoph
Becher, Veronica Andrea
Scheerer, Adrian-Maria
Slaman, Theodore A.
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.