Average order of an arithmetic function
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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- enIn 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) .
- Has abstract
- enIn 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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- enAverage order of an arithmetic function
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- Arithmetic function
- Cambridge University Press
- Category:Arithmetic functions
- Cauchy product
- Continuous function
- Dirichlet series
- Divisor
- Divisor function
- Divisor sum identities
- Divisor summatory function
- Euler's totient function
- Euler constant
- Euler–Mascheroni constant
- Euler product
- Euler totient function
- Extremal orders of an arithmetic function
- Finite field
- Indicator function
- Möbius function
- Möbius inversion
- Monic polynomial
- Monotonic function
- Multiplicative function
- Natural density
- Normal order of an arithmetic function
- Number theory
- Prime factors
- Prime number theorem
- Riemann zeta function
- Ring of polynomials
- Square-free integers
- Undergraduate Texts in Mathematics
- Von Mangoldt function
- Zeta function
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- Average order of an arithmetic function
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- m.04gndm3
- Ordre moyen d'une fonction arithmétique
- Q3355756
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- Category:Arithmetic functions
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