Difference between revisions of "Chebyshev theta function"
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(Created page with "The Chebyshev $\vartheta$ function is $$\vartheta(x) = \displaystyle\sum_{p \leq x} \log p,$$ where $p \leq x$ denotes that $p$ is a prime number less than the real number $x$.") |
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$$\vartheta(x) = \displaystyle\sum_{p \leq x} \log p,$$ | $$\vartheta(x) = \displaystyle\sum_{p \leq x} \log p,$$ | ||
where $p \leq x$ denotes that $p$ is a prime number less than the real number $x$. | where $p \leq x$ denotes that $p$ is a prime number less than the real number $x$. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Chebyshevplotto50.png|Plot of $\vartheta$ on $[0,50]$. | ||
| + | File:Chebyshevplotto100.png|Plot of $\vartheta$ on $[0,100]$. | ||
| + | File:Chebyshevplotto1000.png|Plot of $\vartheta$ on $[0,1000]$. | ||
| + | </gallery> | ||
| + | </div> | ||
Revision as of 04:59, 4 September 2015
The Chebyshev $\vartheta$ function is $$\vartheta(x) = \displaystyle\sum_{p \leq x} \log p,$$ where $p \leq x$ denotes that $p$ is a prime number less than the real number $x$.
- Chebyshevplotto50.png
Plot of $\vartheta$ on $[0,50]$.
- Chebyshevplotto100.png
Plot of $\vartheta$ on $[0,100]$.
- Chebyshevplotto1000.png
Plot of $\vartheta$ on $[0,1000]$.
