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Exponential bound for Euler's zeta function?

  1. Apr 2, 2008 #1
    Let Euler's zeta function be given by

    [tex]
    \sum_{n=1}^{\infty}1/n^s
    [/tex]

    Is there an exponent L which limits the finiteness of

    [tex]
    (\sum_{n=1}^{\infty}1/n^s)^L
    [/tex]

    for the case where s=1?
     
  2. jcsd
  3. Apr 2, 2008 #2

    Gib Z

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    When s=1, that series diverges, so there is no value of L that would make it finite.
     
  4. Apr 3, 2008 #3
    Gib Z,

    The ineffectiveness of an exponential on a diverging sequence should have been obvious to me.
     
  5. Apr 3, 2008 #4

    Gib Z

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    Homework Helper

    Don't worry, we all have brain farts once in a while =]
     
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