| Autor: |
Aistleitner, Christoph, Becher, Verónica, Scheerer, Adrian-Maria, Slaman, Theodore |
| Rok vydání: |
2017 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
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 $(b^n x \mod 1)_{n\geq 0}$ is of asymptotic order $\mathcal{O}(N^{-1/2})$. 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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