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Erdős Sieves and Dynamics
9. Applications to Number Theory
9.2. Squarefree Values of Polynomials
1. Introduction
2. Preliminaries
2.1. Ideals in Number Fields
2.2. Dynamical Systems
3. Sieves and R-free numbers
3.1. Shift Spaces
3.2. Density of R-free numbers
4. Topological Dynamical Systems
5. Sieves with Light Tails
5.1. Repeated Patterns in FR
5.2. Sieves with Strong Light Tails
5.3. Weak and Strong Light Tails
6. A Theory of Sieves
6.1. Minimal Sieves
6.2. Union of Sieves
7. Spectrum and Equivalence of Dynamical Systems
7.1. Equality of Dynamical Systems
7.2. Isomorphisms of Dynamical Systems
7.3. Spectrum Computation
8. XR and R
9. Applications to Number Theory
9.1. Infinite Patterns in FR
9.2. Squarefree Values of Polynomials
9.3. Ergodic Prime Number Theorem for R-free Numbers
References
Index
Dissertation
Erdős Sieves and Dynamics / Francisco Araújo ; supervisor: Prof. Dr. Jürgen Klüners
Entstehung
Paderborn
2026
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