Zeta function Definition and 106 Threads

  1. S

    Recursive formula for zeta function of positive even integers

    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...
  2. Jameson

    What is the Riemann Hypothesis and Why is it Important in Number Theory?

    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
    • Jameson
    • Thread
    • Function Riemann Riemann zeta function Zeta function
    • Replies: 8
    • Forum: Calculus
  3. C

    Calculating values of the zeta function

    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...
  4. T

    How to calculate a zero of the Reimann zeta function?

    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...
  5. W

    Zeta function = vacuum Background?

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

    Is the zeta function a complex mapping onto the infinite sum of 1/j^s terms?

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