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Riemann Zeta function of even numbers

  1. Jul 30, 2011 #1
    Given that

    [tex]\zeta (2n)=\frac{{\pi}^{2n}}{m}[/tex]

    Then how do you find m with respect to n where n is a natural number.

    For

    n=1, m=6
    n=2, m=90
    n=3, m=945
    n=4, m=9450
    n=5, m=93555
    n=6, m=[tex]\frac{638512875}{691}[/tex]
    n=7, m=[tex]\frac{18243225}{2}[/tex]
    n=8, m=[tex]\frac{325641566250}{3617}[/tex]
    n=9, m=[tex]\frac{38979295480125}{43867}[/tex]
    n=10, m=[tex]\frac{1531329465290625}{174611}[/tex]

    But I don't see any pattern.

    Thanks.
     
  2. jcsd
  3. Jul 30, 2011 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    I would find it by consulting wikipedia.
     
  4. Jul 30, 2011 #3
    Thanks.
     
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