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November 8th, 2012, 10:39 PM   #1
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Critical Strip

Hello, everyone!

Here's a nice property of zeta function; I would like to present it as an exercise :

Prove that

Balarka

.
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November 13th, 2012, 12:09 AM   #2
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Re: Critical Strip

Hint : consider the difference and make N =Im[s].
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November 13th, 2012, 02:59 PM   #3
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Re: Critical Strip

Hi Balarka,

One thing I am wondering is why did you call your post "critical strip"? The critical strip is defined for 0<Re(s)<1 right? you seem to be asking about a proprety of Zeta for Re(s)=1 no?
After the answer, using your hint and a well know formula, we can say that since , we reach your conclusion that .
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December 28th, 2012, 11:13 PM   #4
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Re: Critical Strip

Quote:
Originally Posted by Dougy
One thing I am wondering is why did you call your post "critical strip"?
I wanted a nice name for this post but couldn't find one. So, I gave it a name related to it.

Now prove this for where A is any positive constant.

Does this modification makes the name much more proper?

Note: I am back in this forum after a long time so please forgive me for replying in an ancient posts :P
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December 29th, 2012, 04:40 AM   #5
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Re: Critical Strip

WELCOME BACK!

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