# Arithmetic function/Related Articles

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*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.
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## 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.
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### 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.
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### 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.
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- 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.
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- Class field theory [r]: The branch of algebraic number theory which studies the abelian extensions of a number field, or more generally a global or local field.
^{[e]} - Completely multiplicative function [r]:
*Add brief definition or description* - Special function [r]: Various families of solution functions corresponding to cases of the hypergeometric equation or functions used in the equation's study, such as the gamma function.
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