11Pxx Additive number theory
This subtopic studies additive number theory, concerned with sums of integers, additive bases, and the partitioning or representation of numbers.
Specific topics
11P05 Waring's problem and variants
Overview
11P05 addresses waring's problem and variants in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Waring's problem and variants (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for waring's problem and variants
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P32 Goldbach-type theorems
Overview
11P32 addresses goldbach-type theorems in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Goldbach-type theorems (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for goldbach-type theorems
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P55 Applications of the Hardy-Littlewood method
Overview
11P55 addresses applications of the hardy-littlewood method in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Applications of the Hardy-Littlewood method (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for applications of the hardy-littlewood method
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P70 Inverse problems of additive number theory
Overview
11P70 addresses inverse problems of additive number theory in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Inverse problems of additive number theory (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for inverse problems of additive number theory
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P81 Elementary theory of partitions
Overview
11P81 addresses elementary theory of partitions in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Elementary theory of partitions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for elementary theory of partitions
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P82 Analytic theory of partitions
Overview
11P82 addresses analytic theory of partitions in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Analytic theory of partitions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for analytic theory of partitions
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P83 Partitions; congruences and congruential restrictions
Overview
11P83 addresses partitions; congruences and congruential restrictions in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Partitions; congruences and congruential restrictions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for partitions; congruences and congruential restrictions
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks
11P84 Partition identities; Bell numbers
Overview
11P84 addresses partition identities; bell numbers in additive number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Partition identities; Bell numbers (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for partition identities; bell numbers
- Techniques that combine asymptotic estimates with structural arguments
- Connections to adjacent themes in arithmetic, analysis, and computation
Typical Uses
Used to organize advanced proofs, benchmark conjectures against known results, and build pathways from foundational lemmas to research-level statements.
Applications
- Core theoretical development in number theory
- Algorithmic and computational experimentation
- Cross-links to algebraic geometry, automorphic forms, and cryptography
References
Recommended Textbooks