11Yxx Computational number theory
This subtopic studies computational number theory, focusing on algorithms, complexity, and practical methods for solving arithmetic problems.
Specific topics
11Y05 Factorization
Overview
11Y05 studies factorization within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Factorization (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for factorization
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y11 Primality
Overview
11Y11 studies primality within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Primality (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for primality
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y16 Number-theoretic algorithms; complexity
Overview
11Y16 studies number-theoretic algorithms; complexity within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Number-theoretic algorithms; complexity (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for number-theoretic algorithms; complexity
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y35 Analytic computations
Overview
11Y35 studies analytic computations within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Analytic computations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for analytic computations
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y40 Algebraic number theory computations
Overview
11Y40 studies algebraic number theory computations within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Algebraic number theory computations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for algebraic number theory computations
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y50 Computer solution of Diophantine equations
Overview
11Y50 studies computer solution of diophantine equations within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Computer solution of Diophantine equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for computer solution of diophantine equations
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y55 Calculation of integer sequences
Overview
11Y55 studies calculation of integer sequences within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Calculation of integer sequences (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for calculation of integer sequences
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y60 Evaluation of number-theoretic constants
Overview
11Y60 studies evaluation of number-theoretic constants within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Evaluation of number-theoretic constants (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for evaluation of number-theoretic constants
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y65 Continued fraction calculations
Overview
11Y65 studies continued fraction calculations within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Continued fraction calculations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for continued fraction calculations
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks
11Y70 Values of arithmetic functions; tables
Overview
11Y70 studies values of arithmetic functions; tables within computational number theory. It highlights core definitions, key theorem patterns, and methods that connect structural and computational viewpoints.
Related Wikipedia Page
Values of arithmetic functions; tables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and examples for values of arithmetic functions; tables
- Interactions between algebraic structures, analytic estimates, and effective computation
- How local results and global heuristics inform each other in modern number theory
Typical Uses
Used to select proof frameworks, compare equivalent formulations, and support research-grade computation and verification in number-theoretic work.
Applications
- Foundational progress in arithmetic and field theory
- Algorithm design, complexity analysis, and implementation
- Links to coding theory, logic, and cryptographic methods
References
Recommended Textbooks