About: Average order of an arithmetic function

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In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let be an arithmetic function. We say that an average order of is if as tends to infinity. It is conventional to choose an approximating function that is continuous and monotone. But even so an average order is of course not unique. In cases where the limit exists, it is said that has a mean value (average value) .

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rdfs:label	Average order of an arithmetic function (en)
rdfs:comment	In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let be an arithmetic function. We say that an average order of is if as tends to infinity. It is conventional to choose an approximating function that is continuous and monotone. But even so an average order is of course not unique. In cases where the limit exists, it is said that has a mean value (average value) . (en)
sameAs	Average order of an arithmetic function Average order of an arithmetic function
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Math dbt:Thinsp dbt:Hardy_and_Wright
Subject	Arithmetic functions
Link from a Wikipage to an external page	https://archive.org/details/introductiontoan00apos_0
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Average_order_of_an_arithmetic_function?oldid=1056327075&ns=0
Wikipage page ID	18760872 (xsd:integer)
page length (characters) of wiki page	17636 (xsd:nonNegativeInteger)
Wikipage revision ID	1056327075 (xsd:integer)
Link from a Wikipage to another Wikipage	List of zeta functions Möbius function Möbius inversion formula Normal order of an arithmetic function Number theory Undergraduate Texts in Mathematics Arithmetic function Monotonic function Von Mangoldt function Cambridge University Press Arithmetic functions Cauchy product Dirichlet series Divisor Divisor function Divisor sum identities Divisor summatory function Prime number Prime number theorem Square-free integer Continuous function Finite field Indicator function Extremal orders of an arithmetic function Monic polynomial Euler's constant Euler's totient function Euler product Multiplicative function Natural density Polynomial ring Riemann zeta function
has abstract	In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let be an arithmetic function. We say that an average order of is if as tends to infinity. It is conventional to choose an approximating function that is continuous and monotone. But even so an average order is of course not unique. In cases where the limit exists, it is said that has a mean value (average value) . (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Average_order_of_an_arithmetic_function
is Wikipage redirect of	Mean value of an arithmetic function
is Link from a Wikipage to another Wikipage of	Möbius function Normal order of an arithmetic function Arithmetic function Jordan's totient function Divisor function Divisor sum identities Extremal orders of an arithmetic function Mean value of an arithmetic function
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Average_order_of_an_arithmetic_function

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