Difference between revisions of "Chebyshev theta function"

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<gallery>
 
<gallery>
 
File:Chebyshevplotfrom0to50.png|Plot of $\vartheta$ on $[0,50]$.
 
File:Chebyshevplotfrom0to50.png|Plot of $\vartheta$ on $[0,50]$.
File:Chebyshevthetaplotto100.png|Plot of $\vartheta$ on $[0,100]$.
+
File:Chebyshevplotfrom0to100.png|Plot of $\vartheta$ on $[0,100]$.
 
File:Chebyshevthetaplotto1000.png|Plot of $\vartheta$ on $[0,1000]$.
 
File:Chebyshevthetaplotto1000.png|Plot of $\vartheta$ on $[0,1000]$.
 
</gallery>
 
</gallery>

Revision as of 02:11, 28 November 2016

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 $x$.

Number theory functions