simplemind
JF-Expert Member
- Apr 10, 2009
- 16,418
- 9,206
Clay millennium prize ya dollar milioni moja kwa yeyeto atakaye thibitisha Riemann hypothesis.
What is Riemann Hypothesis?
The Riemann Hypothesis is a statement about the locations of zeros of a certain function. That function is called the Riemann Zeta Function, denoted ζ(s), where s∈C is a complex variable. For R(s)>1, the function is defined as
ζ(s)=∑1/s^n(sum to infinity)
Through a process called meromorphic continuation, one can extend this function to an analytic function on almost the entire complex plane.
It turns out that ζ(s) is zero at every negative even integer. These are the so-called 'trivial zeros'. The Riemann Hypothesis is simply the statement that all of the other zeros of ζ(s) are on the so-called critical line R(s)=1/2 . (It is known that all of the other zeros are in the 'critical strip', which is simply {s∈C:0<R(s)<1}
Hapa kazi tu.
What is Riemann Hypothesis?
The Riemann Hypothesis is a statement about the locations of zeros of a certain function. That function is called the Riemann Zeta Function, denoted ζ(s), where s∈C is a complex variable. For R(s)>1, the function is defined as
ζ(s)=∑1/s^n(sum to infinity)
Through a process called meromorphic continuation, one can extend this function to an analytic function on almost the entire complex plane.
It turns out that ζ(s) is zero at every negative even integer. These are the so-called 'trivial zeros'. The Riemann Hypothesis is simply the statement that all of the other zeros of ζ(s) are on the so-called critical line R(s)=1/2 . (It is known that all of the other zeros are in the 'critical strip', which is simply {s∈C:0<R(s)<1}
Hapa kazi tu.
