تقرير
Correlations of the Thue--Morse sequence
| العنوان: | Correlations of the Thue--Morse sequence |
|---|---|
| المؤلفون: | Baake, Michael, Coons, Michael |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Number Theory, 37B10, 52C23 |
| الوصف: | The pair correlations of the Thue--Morse sequence and system are revisited, with focus on asymptotic results on various means. First, it is shown that all higher-order correlations of the Thue--Morse sequence with general real weights are effectively determined by a single value of the balanced $2$-point correlation. As a consequence, we show that all odd-order correlations of the balanced Thue--Morse sequence vanish, and that, for any even $n$, the $n$-point correlations of the balanced Thue--Morse sequence have mean value zero, as do their absolute values, raised to an arbitrary positive power. All these results also apply to the entire Thue--Morse system. We finish by showing how the correlations of the Thue--Morse system with general real weights can be derived from the balanced $2$-point correlations. Comment: 18 pages, revised version, with minor additions and improvements |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2209.07102 |
| رقم الأكسشن: | edsarx.2209.07102 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |