56 HomeYamamoto and the Secret Admirers
Neal Stephenson


Riemann Zeta Function
In 1740 Leonhard Euler introduced the zeta function as an infinite series.
In 1859 the German mathematician Bernhard Riemann treated the Zeta Function as a function of a complex variable z.
Where z = a + bi
a = Re(z) the real part

bi = Im(z) the imaginary part

For this reason this form of Zeta Function is known as a Riemann Zeta Function.

Related to the Riemann Zeta Function is the Riemann hypothesis which to this date still remains unproved.
The function has no zeros in Re(z) ≥ 1; and for Re(z) ≤ 0 it has zeros at z = -2, -4, -6, ...; but for 0 < Re(z) < 1 there is an infinite number of zeroes, which are called nontrivial zeroes.
The hypothesis is that all the nontrivial zeros oflie on the line Re(z) = ½.        

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