تقرير
Are prime numbers and quadratic residues random?
| العنوان: | Are prime numbers and quadratic residues random? |
|---|---|
| المؤلفون: | Blank, Michael |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Number Theory, Primary: 37A44, Secondary: 37A35, 11N05, 11K65 |
| الوصف: | Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. It is enough to mention such famous names as V.I. Arnold, M. Katz, Yu.G. Sinai and T. Tao. Unfortunately, it all comes down to various, although often very non-trivial and elegant, heuristics. A new analytical approach is proposed to address the issue of randomness/complexity of an individual deterministic sequence. As an application, it demonstrates the expected high complexity of quadratic residues and the unexpectedly low complexity in the case of primes. Technically, the proposed approach is based on a fundamentally new construction of the entropy of a single trajectory of a dynamical system, which in a certain sense occupies an intermediate position between the classical metric Kolmogorov-Sinai entropy and topological entropy. Comment: 18 pages. The normalization of local entropy has been changed and a number of results and estimates have been improved |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.04490 |
| رقم الأكسشن: | edsarx.2403.04490 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |