Mangoldt summatory function
It is defined thus:
where is the Mangoldt function.
Note that we do not have to worry that the inequality above is ambiguous, because is only non-zero for natural . So no matter whether we take it to mean r is real, integer or natural, the result is the same because we just get a lot of zeros added to our answer.
The prime number theorem, which states:
and then the prime number theorem is also equivalent to:
which turns out to be easier to work with than the original form.
|Title||Mangoldt summatory function|
|Date of creation||2013-03-22 13:27:16|
|Last modified on||2013-03-22 13:27:16|
|Last modified by||mathcam (2727)|
|Synonym||von Mangoldt summatory function|