# Exponential bound for Euler's zeta function?

1. Apr 2, 2008

### Loren Booda

Let Euler's zeta function be given by

$$\sum_{n=1}^{\infty}1/n^s$$

Is there an exponent L which limits the finiteness of

$$(\sum_{n=1}^{\infty}1/n^s)^L$$

for the case where s=1?

2. Apr 2, 2008

### Gib Z

When s=1, that series diverges, so there is no value of L that would make it finite.

3. Apr 3, 2008

### Loren Booda

Gib Z,

The ineffectiveness of an exponential on a diverging sequence should have been obvious to me.

4. Apr 3, 2008

### Gib Z

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