Skip to main content
MathOverflow

Return to Question

fixed LaTeX and reverted to standard notations for sums over primes
Source Link
Peter Humphries
Peter Humphries
  • 8.4k
  • 3
  • 51
  • 75

Convergence of the series 1/p^s$\sum_p p^{-s}$ (p$p$ prime and s>1$s>1$)

I know that $\sum_{p\in\mathbb{P}} \frac{1}{p^s}$$\sum_p p^{-s}$, (s>1)$s>1$, converges. Now, I define $J(s) = \sum_{p\in\mathbb{P}} \frac{1}{p^s}$$J(s) = \sum_p p^{-s}$. Are there any "well known"known" values for J(2)$J(2)$,J(3) $J(3)$,J(4) $J(4)$, etc? like weWe all know that $\zeta(2)= \frac{\pi^2}{6}$, $\zeta(4)=\frac{\pi^4}{90}$, etc.

Convergence of the series 1/p^s (p prime and s>1)

I know that $\sum_{p\in\mathbb{P}} \frac{1}{p^s}$ (s>1) converges. Now, I define $J(s) = \sum_{p\in\mathbb{P}} \frac{1}{p^s}$. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that $\zeta(2)= \frac{\pi^2}{6}$, $\zeta(4)=\frac{\pi^4}{90}$, etc.

Convergence of the series $\sum_p p^{-s}$ ($p$ prime and $s>1$)

I know that $\sum_p p^{-s}$, $s>1$, converges. Now, I define $J(s) = \sum_p p^{-s}$. Are there any "well known" values for $J(2)$, $J(3)$, $J(4)$, etc? We all know that $\zeta(2)= \frac{\pi^2}{6}$, $\zeta(4)=\frac{\pi^4}{90}$, etc.

Added LaTeX
Source Link
Johannes Hahn
Johannes Hahn
  • 9.7k
  • 2
  • 33
  • 66

Convergence of the summationseries 1/p^s (p prime and s>1)

I know that the summation 1/p^s $\sum_{p\in\mathbb{P}} \frac{1}{p^s}$ (s>1 and p prime) converges. Now, I define J(s) = summation 1/p^s$J(s) = \sum_{p\in\mathbb{P}} \frac{1}{p^s}$. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that zeta(2)= (pi^2)/6$\zeta(2)= \frac{\pi^2}{6}$, zeta(4)= (pi^4)/90$\zeta(4)=\frac{\pi^4}{90}$, etc.

Convergence of the summation 1/p^s (p prime and s>1)

I know that the summation 1/p^s (s>1 and p prime) converges. Now, I define J(s) = summation 1/p^s. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that zeta(2)= (pi^2)/6, zeta(4)= (pi^4)/90, etc.

Convergence of the series 1/p^s (p prime and s>1)

I know that $\sum_{p\in\mathbb{P}} \frac{1}{p^s}$ (s>1) converges. Now, I define $J(s) = \sum_{p\in\mathbb{P}} \frac{1}{p^s}$. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that $\zeta(2)= \frac{\pi^2}{6}$, $\zeta(4)=\frac{\pi^4}{90}$, etc.

deleted 2 characters in body; edited tags
Source Link
Charles
Charles
  • 9.1k
  • 1
  • 38
  • 76

I know that the summation 1/p^s (s>1 and p prime) converges. Now, I define J(s) = summation 1/p^s. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that zeta(2)= (pie^2pi^2)/6, zeta(4)= (pie^4pi^4)/90, etc.

I know that the summation 1/p^s (s>1 and p prime) converges. Now, I define J(s) = summation 1/p^s. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that zeta(2)= (pie^2)/6, zeta(4)= (pie^4)/90, etc.

I know that the summation 1/p^s (s>1 and p prime) converges. Now, I define J(s) = summation 1/p^s. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that zeta(2)= (pi^2)/6, zeta(4)= (pi^4)/90, etc.

Source Link
bulai
bulai
  • 101
  • 3