How are zeros of Riemann Zeta function related to distribution of prime numbers? What does 'proving all non-trivial zeros lie on the critical line' say about distribution of zeros on the critical
![SOLVED:The Riemann zeta-function ζis defined by ζ(x) = ∑n = 1^∞ (1)/(n^x) and is used in number theory to study the distribution of prime numbers. What is the domain of ζ? SOLVED:The Riemann zeta-function ζis defined by ζ(x) = ∑n = 1^∞ (1)/(n^x) and is used in number theory to study the distribution of prime numbers. What is the domain of ζ?](https://cdn.numerade.com/previews/ba90844f-6fa8-42d7-811e-85c42c58a773_large.jpg)
SOLVED:The Riemann zeta-function ζis defined by ζ(x) = ∑n = 1^∞ (1)/(n^x) and is used in number theory to study the distribution of prime numbers. What is the domain of ζ?
![The holy grail of mathematics: animated visualization of the Riemann Zeta zeros | by Vladimir Ilievski | Towards Data Science The holy grail of mathematics: animated visualization of the Riemann Zeta zeros | by Vladimir Ilievski | Towards Data Science](https://miro.medium.com/max/1400/1*WAX3l1Mmc-fUEKOHnoyHoA.png)