![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?
![complex numbers - Show how to calculate the Riemann zeta function for the first non-trivial zero - Mathematics Stack Exchange complex numbers - Show how to calculate the Riemann zeta function for the first non-trivial zero - Mathematics Stack Exchange](https://i.stack.imgur.com/84i9J.png)
complex numbers - Show how to calculate the Riemann zeta function for the first non-trivial zero - Mathematics Stack Exchange
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
![Riemann's functional equation for the zeta function | Functions of a Complex Variable | Mathematics | MIT OpenCourseWare Riemann's functional equation for the zeta function | Functions of a Complex Variable | Mathematics | MIT OpenCourseWare](https://ocw.mit.edu/courses/18-112-functions-of-a-complex-variable-fall-2008/b039f5767c57072ec922e985c5e3749a_18-112f08.jpg)