Difference between revisions of "Chebyshev psi function"
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(Created page with "The Chebyshev $\psi$ function is $$\psi(x) = \displaystyle\sum_{p^k \leq x} \log p = \displaystyle\sum_{n \leq x} \Lambda(n),$$ where $\Lambda$ denotes the Mangoldt functio...") |
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$$\psi(x) = \displaystyle\sum_{p^k \leq x} \log p = \displaystyle\sum_{n \leq x} \Lambda(n),$$ | $$\psi(x) = \displaystyle\sum_{p^k \leq x} \log p = \displaystyle\sum_{n \leq x} \Lambda(n),$$ | ||
where $\Lambda$ denotes the [[Mangoldt function]]. | where $\Lambda$ denotes the [[Mangoldt function]]. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Chebyshevpsiplotto100.png|Plot of $\psi$ on $[0,100]$. | ||
| + | File:Chebyshevpsiplotto1000.png|Plot of $\psi$ on $[0,1000]$. | ||
| + | </gallery> | ||
| + | </div> | ||
Revision as of 04:02, 4 September 2015
The Chebyshev $\psi$ function is $$\psi(x) = \displaystyle\sum_{p^k \leq x} \log p = \displaystyle\sum_{n \leq x} \Lambda(n),$$ where $\Lambda$ denotes the Mangoldt function.
Plot of $\psi$ on $[0,100]$.
Plot of $\psi$ on $[0,1000]$.
