Extremal orders of an arithmetic function information
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.[1]: 80 Here, and denote the limit inferior and limit superior, respectively.
The subject was first studied systematically by Ramanujan starting in 1915.[1]: 87
^ ab
Tenenbaum, Gérald (1995). Introduction to Analytic and Probabilistic Number Theory. Cambridge studies in advanced mathematics. Vol. 46. Cambridge University Press. ISBN 0-521-41261-7.
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