Exponential bound for Euler's zeta function?

  • #1
3,073
3

Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
Gib Z
Homework Helper
3,344
4
When s=1, that series diverges, so there is no value of L that would make it finite.
 
  • #3
3,073
3
Gib Z,

The ineffectiveness of an exponential on a diverging sequence should have been obvious to me.
 
  • #4
Gib Z
Homework Helper
3,344
4
Don't worry, we all have brain farts once in a while =]
 

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