Difference between revisions of "Riemann zeta"

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__NOTOC__
 
Consider the function $\zeta$ defined by the series
 
Consider the function $\zeta$ defined by the series
 
$$\zeta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n^z},$$
 
$$\zeta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n^z},$$
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=Videos=
 
=Videos=
 
[https://www.youtube.com/watch?v=ZlYfEqdlhk0&list=PL32446FDD4DA932C9 Riemann Zeta function playlist]<br />
 
[https://www.youtube.com/watch?v=ZlYfEqdlhk0&list=PL32446FDD4DA932C9 Riemann Zeta function playlist]<br />
 
=References=
 
* {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|next=Euler product for Riemann zeta}}: § Introduction (1)
 
  
 
=External links=
 
=External links=
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*[http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]
 
*[http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]
 
*[http://www.dtc.umn.edu/~odlyzko/zeta_tables/ Andrew Odlyzko: Tables of zeros of the Riemann zeta function]
 
*[http://www.dtc.umn.edu/~odlyzko/zeta_tables/ Andrew Odlyzko: Tables of zeros of the Riemann zeta function]
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=References=
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* {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|next=Euler product for Riemann zeta}}: § Introduction (1)
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 19:47, 9 June 2016

Consider the function $\zeta$ defined by the series $$\zeta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n^z},$$ which is valid for $\mathrm{Re}(z)>1$.

Properties

Euler product for Riemann zeta Laurent series of the Riemann zeta function Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta

Videos

Riemann Zeta function playlist

External links

References