Arithmetic function/Related Articles: Difference between revisions
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imported>Richard Pinch (→Other related topics: Formal Dirichlet series, Wiener-Ikehara theorem) |
imported>Jitse Niesen (add examples from main page) |
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{{r|Average order of an arithmetic function}} | {{r|Average order of an arithmetic function}} | ||
{{r|Normal order of an arithmetic function}} | {{r|Normal order of an arithmetic function}} | ||
===Totally multiplicative functions=== | |||
{{r|Dirichlet character}} | |||
===Multiplicative functions=== | |||
{{r|Totient function}} | |||
{{r|Jordan's totient function}} | |||
{{r|Lambda function}} | |||
{{r|Möbius function}} | |||
==Other related topics== | ==Other related topics== | ||
Latest revision as of 06:02, 15 June 2009
- See also changes related to Arithmetic function, or pages that link to Arithmetic function or to this page or whose text contains "Arithmetic function".
Parent topics
- Number theory [r]: The study of integers and relations between them. [e]
Subtopics
- Average order of an arithmetic function [r]: A simple or well-known function, usually continuous and montonic, which on average takes the same or closely approximate values as a given arithmetic function. [e]
- Normal order of an arithmetic function [r]: A simple or well-known function, usually continuous and montonic, which "usually" takes the same or closely approximate values as a given arithmetic function. [e]
Totally multiplicative functions
- Dirichlet character [r]: A group homomorphism on the multiplicative group in modular arithmetic extended to a multiplicative function on the positive integers. [e]
Multiplicative functions
- Totient function [r]: The number of integers less than or equal to and coprime to a given integer. [e]
- Jordan's totient function [r]: A generalisation of Euler's totient function. [e]
- Lambda function [r]: The exponent of the multiplicative group modulo an integer. [e]
- Möbius function [r]: Arithmetic function which takes the values -1, 0 or +1 depending on the prime factorisation of its input n. [e]
- Formal Dirichlet series [r]: Add brief definition or description
- Wiener-Ikehara theorem [r]: A Tauberian theorem used in number theory to relate the behaviour of a real sequence to the analytic properties of the associated Dirichlet series. [e]