Riemann Hypothesis

Yesterday, I said that I would do a post on the Riemann Hypothesis, so here we are now.

There is a function with the name of the Riemann Zeta Function, named after Bernhard Riemann. The Riemann Hypothesis states that the Riemann zeta function has zeroes only at the negative even integers and complex numbers with the real part of 1/2. So, in explanation, ζ (s) is a function where the argument s may be any complex number not equal to one, and its zeroes are at points where s is a negative even integer, like -2, -4, -6, -8 and so on. These are trivial zeroes.

The non-trivial zeroes of the Riemann Zeta Function have a real part of 1/2. So if the hypothesis is true, then all non-trivial zeroes take a form of 1/2 + it, where t is a real number and i is the imaginary number.

There’s actually a formula for the Riemann Zeta Function:

{\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots }

For more info, visit this website, Wikipedia.

Maybe, I’ll go more in depth about the Riemann Hypothesis, but not now.

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