Difference between revisions of "First Chebyshev function"

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* [[Prime-counting function]]: Denoted <math>\pi(x)</math>, this simply counts the number of primes less than or equal to <math>x</math>.
 
* [[Prime-counting function]]: Denoted <math>\pi(x)</math>, this simply counts the number of primes less than or equal to <math>x</math>.
 
* [[Second Chebyshev function]]: A similar summation, but this time of the [[von Mangoldt function]] over all prime powers less than or equal to <math>x</math>.
 
* [[Second Chebyshev function]]: A similar summation, but this time of the [[von Mangoldt function]] over all prime powers less than or equal to <math>x</math>.
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===Modular versions===
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* [[Modular first Chebyshev function]]
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* [[Modular second Chebyshev function]]

Latest revision as of 01:25, 7 May 2009

This article is about a function defined on positive reals (and in particular, natural numbers) obtained as the summatory function of an arithmetic function.
View other such summations

Definition

Let be a positive real number. The first Chebyshev function of , denoted or , is defined as:

,

where the sum is only over the prime numbers less than or equal to .

Relation with other counting functions

Modular versions