Zeta function Definition and 111 Threads

Hello, I was trying recently to find a derivative of a zeta function but finally I failed. Can anyone show me a way to find it, I'm more interested in the way of finding it rather than clear aprox. solution. Thanks,

They claim that the trivial 0s (zeta(z)=0) occur when z is a negative odd integer (with no imaginary component). But it seems obviously wrong. Take z=-2 zeta(-2)=1+1/(2^-2)+1/(3^-2)... =1+4+9... Obviously this series will not equal 0. Where have I gone wrong? Have I misunderstood...

I was trying to explain to my family last night why 1 is not generally defined as a prime number and I thought of the Zeta Function. There is the standard way to write it, (1)\zeta(s)=\sum_{n=1}^{\infty}n^{-s} but then there is also the Euler product formula...

Hello, i would like to know the definiton of epstein zeta function and its zeros,i would like to know if s is a zero then s* is also a zero and what would be the functional equation that the Epstein function satisfy...thanks.

So it is well-known that for n=2,3,... the following equation holds \zeta(n)=\int_{x_{n}=0}^{1}\int_{x_{n-1}=0}^{1}\cdot\cdot\cdot\int_{x_{1}=0}^{1}\left(\frac{1}{1-\prod_{k=1}^{n}x_{k}}\right)dx_{1}\cdot\cdot\cdot dx_{n-1}dx_{n} My question is how can this relation be extended to...

I was working with Fourier series and I found the following recursive formula for the zeta function: \frac{p \\ \pi^{2p}}{2p+1} + \sum_{k=1}^{p} \frac{(2p)! (-1)^k \pi^{2(p-k)}}{(2(p-k)+1)!} \zeta(2k) = 0 where [itex]\zeta(k)[/tex] is the Riemann zeta function and p is a positive integer. I...

I have read what MathWorld has to offer on this and I am extremely confused. Could someone please explain this as simply as possible? Or then again maybe MathWorld already did that. Also, why is this function so important? Many thanks, Jameson

Hi Group, I appologise in advance. My maths knowledge is pretty bad, so some of what I say may not make sense. I'm interested in the Riemann Zeta function, and more specificaly, the Riemann zero's. I'm not trying to prove it, I just want to calculate some of the values. And that's what...

I've read several recent books on the RH for the lay audience. However, none show how to actually calulate a zero of the Reimann zeta function. For example, how does one calculate: 14.134725142 21.022039639 25.010857580 30.424876126 32.935061588 I would really like to know an...

Here is a paper that has some interesting concepts: http://arxiv.org/abs/hep-th/0412217 Is this possible/probable? :confused:

I came across this at another website which usually does not delve into mathematics at all.