Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    Don't worry, we all have brain farts once in a while =]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook