11Nxx Multiplicative number theory
This subtopic studies multiplicative number theory, including Dirichlet series, primes, and multiplicative arithmetic functions and their distributions.
Specific topics
11N05 Distribution of primes
Overview
11N05 addresses distribution of primes in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Distribution of primes (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for distribution of primes
- 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
11N13 Primes in progressions
Overview
11N13 addresses primes in progressions in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Primes in progressions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for primes in progressions
- 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
11N25 Distribution of integers with specified multiplicative constraints
Overview
11N25 addresses distribution of integers with specified multiplicative constraints in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Distribution of integers with specified multiplicative constraints (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for distribution of integers with specified multiplicative constraints
- 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
11N32 Primes represented by polynomials
Overview
11N32 addresses primes represented by polynomials in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Primes represented by polynomials (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for primes represented by polynomials
- 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
11N35 Sieves
Overview
11N35 addresses sieves in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Sieves (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for sieves
- 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
11N36 Applications of sieve methods
Overview
11N36 addresses applications of sieve methods in multiplicative 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 sieve methods (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for applications of sieve methods
- 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
11N37 Asymptotic results on arithmetic functions
Overview
11N37 addresses asymptotic results on arithmetic functions in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Asymptotic results on arithmetic functions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for asymptotic results on arithmetic functions
- 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
11N45 Asymptotic results on counting functions for primes
Overview
11N45 addresses asymptotic results on counting functions for primes in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Asymptotic results on counting functions for primes (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for asymptotic results on counting functions for primes
- 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
11N56 Rate of growth of arithmetic functions
Overview
11N56 addresses rate of growth of arithmetic functions in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Rate of growth of arithmetic functions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for rate of growth of arithmetic functions
- 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
11N60 Distribution functions for arithmetic functions
Overview
11N60 addresses distribution functions for arithmetic functions in multiplicative number theory. It emphasizes rigorous definitions, main theorem families, and analytic or algebraic techniques used in current number-theory practice.
Related Wikipedia Page
Distribution functions for arithmetic functions (Wikipedia)
Useful Links
Key Ideas
- Standard formulations and canonical examples for distribution functions for arithmetic functions
- 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