- #1
eljose
- 492
- 0
let be the Chebyshev function:
[tex] \psi(x)= x- \sum_{\rho} \frac{ x^{\rho}}{\rho}+C-log(1-x^{2}) [/tex] (1)
Where the sum is over the Non trivial zeros of [tex] \zeta(s)[/tex]
then we have that [tex] \psi(n) -\psi(n-1)=\Lambda (n) [/tex] where the Lambda function is only nonzero witha value of log(p) for n=p^{k} with k a positive integer...my question is.. if we use (1) to calculate Chebyshev function..couldn't we get an expression for the log(p)?..thanks.
[tex] \psi(x)= x- \sum_{\rho} \frac{ x^{\rho}}{\rho}+C-log(1-x^{2}) [/tex] (1)
Where the sum is over the Non trivial zeros of [tex] \zeta(s)[/tex]
then we have that [tex] \psi(n) -\psi(n-1)=\Lambda (n) [/tex] where the Lambda function is only nonzero witha value of log(p) for n=p^{k} with k a positive integer...my question is.. if we use (1) to calculate Chebyshev function..couldn't we get an expression for the log(p)?..thanks.