About: Extremal orders of an arithmetic function

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In mathematics, specifically in number theory, the extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n) is a non-decreasing function that is ultimately positive and we say that m is a minimal order for f. Similarly if M(n) is a non-decreasing function that is ultimately positive and we say that M is a maximal order for f. Here, and denote the limit inferior and limit superior, respectively. The subject was first studied systematically by Ramanujan starting in 1915.

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  • In mathematics, specifically in number theory, the extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n) is a non-decreasing function that is ultimately positive and we say that m is a minimal order for f. Similarly if M(n) is a non-decreasing function that is ultimately positive and we say that M is a maximal order for f. Here, and denote the limit inferior and limit superior, respectively. The subject was first studied systematically by Ramanujan starting in 1915. (en)
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  • In mathematics, specifically in number theory, the extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n) is a non-decreasing function that is ultimately positive and we say that m is a minimal order for f. Similarly if M(n) is a non-decreasing function that is ultimately positive and we say that M is a maximal order for f. Here, and denote the limit inferior and limit superior, respectively. The subject was first studied systematically by Ramanujan starting in 1915. (en)
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  • Extremal orders of an arithmetic function (en)
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