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Riemann zeta function

The Riemann zeta function ζ is defined by

and is used in number theory to study the distribution of prime numbers.

 

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Explanation

For natural numbers you write the function as

and for complex numbers as

 

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Examples

With this, the French nathematician Jean Baptiste Fourier calculated

With this, the Swiss mathematician Leonhard Euler calculated

 

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History The German mathematician Bernhard Riemann (1826 - 1866) defined the Zeta function.

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