11Kxx Probabilistic number theory
This subtopic studies probabilistic number theory, emphasizing distributional questions, random models, and statistical behavior of arithmetic functions.
Specific topics
11K06 General theory of distribution modulo 1
Overview
11K06 studies general theory of distribution modulo 1 within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
General theory of distribution modulo 1 (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for general theory of distribution modulo 1
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K16 Normal numbers, radix expansions
Overview
11K16 studies normal numbers, radix expansions within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Normal numbers, radix expansions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for normal numbers, radix expansions
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K31 Special sequences
Overview
11K31 studies special sequences within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Special sequences (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for special sequences
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K36 Well-distributed sequences and other variations
Overview
11K36 studies well-distributed sequences and other variations within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Well-distributed sequences and other variations (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for well-distributed sequences and other variations
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K38 Irregularities of distribution, discrepancy
Overview
11K38 studies irregularities of distribution, discrepancy within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Irregularities of distribution, discrepancy (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for irregularities of distribution, discrepancy
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K41 Continuous, $p$-adic and abstract analogues
Overview
11K41 studies continuous, p-adic and abstract analogues within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Continuous, p-adic and abstract analogues (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for continuous, p-adic and abstract analogues
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K45 Pseudo-random numbers; Monte Carlo methods
Overview
11K45 studies pseudo-random numbers; monte carlo methods within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Pseudo-random numbers; Monte Carlo methods (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for pseudo-random numbers; monte carlo methods
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K50 Metric theory of continued fractions
Overview
11K50 studies metric theory of continued fractions within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Metric theory of continued fractions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for metric theory of continued fractions
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K55 Metric theory of other algorithms and expansions
Overview
11K55 studies metric theory of other algorithms and expansions within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Metric theory of other algorithms and expansions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for metric theory of other algorithms and expansions
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K60 Diophantine approximation
Overview
11K60 studies diophantine approximation within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Diophantine approximation (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for diophantine approximation
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K65 Arithmetic functions
Overview
11K65 studies arithmetic functions within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Arithmetic functions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for arithmetic functions
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks
11K70 Harmonic analysis and almost periodicity
Overview
11K70 studies harmonic analysis and almost periodicity within probabilistic number theory. It focuses on central definitions, foundational theorem patterns, and techniques that connect structure, computation, and asymptotic behavior.
Related Wikipedia Page
Harmonic analysis and almost periodicity (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and examples for harmonic analysis and almost periodicity
- Core proof tools used in modern number-theoretic research
- Interactions with algebraic, analytic, and computational methods
Typical Uses
Used to frame precise research questions, compare equivalent formulations, and select effective proof or computation strategies in advanced number theory.
Applications
- Development of core theory in arithmetic and analysis
- Algorithmic and computational investigations
- Cross-disciplinary links to algebraic geometry, dynamics, and cryptography
References
Recommended Textbooks