7
$\begingroup$

What do we know about the generating function of $\chi(n)$ (A010051) $$ f(x) = \sum_{n=0}^\infty \chi(n)x^n = \sum_{p\text{ prime}} x^p $$ for $\chi(n)$ the characteristic function of the primes:

$$ \chi(n) = \begin{cases} 1, & \text{if $n$ is prime}\\ 0, & \text{otherwise} \end{cases} $$ Are there some references I could take a look at?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Depends on what you're looking for. For example, if $0<x<1$ you can write $\int_1^{\infty} \pi(t) x^t dt = f(x)/(-\log x)$ and so you can understand $f(x)$ by putting in information on $\pi(t)$. $\endgroup$
    – Lucia
    Commented Dec 11, 2013 at 16:40
  • $\begingroup$ See math.stackexchange.com/questions/602706/… for answers. $\endgroup$
    – Dietrich Burde
    Commented Dec 11, 2013 at 18:37

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .