The Riemann hypothesis

The Riemann hypothesis is one of the most famous and important unsolved problems in number theory. It states that,all the non-trivial zeros of the Riemann zeta function have real part equal to $1/2$. 

The Riemann zeta function is defined by the given relation for any complex number s that is not equal to $1$. 

It has many implications for the distribution of prime numbers and other arithmetic functions.