Re: [PrimeNumbers] Question about the zeta function...
- On Mon, 4 Jul 2005, Jeffrey N. Cook wrote:
> I am a novice with the Zeta Function. Could someone help me understandThis expression for the zeta function only converges when the real
> If I set S = 1, and calculate up to 1/7 and 1/7 only,
> Z(s) = 1 + 1/2^s + 1/3^s + 1/4^s + 1/5^s + 1/6^s + 1/7^s
part of s is greater than one. In Calculus this was called the
"p-test" (at least in the books I use).
> Is this what is meant "that no zeros could lie on the line Re(z) =Nope. That refers to the analytic continuation of the sum above--that
> 1" ? Does S need to be greater than 1 here?
means there is a function that converges on most of the complex plane
that agrees with the sum above (where it converges). This continuation is
called the Riemann zeta function and its the one that all the talk is