November 8th, 2012, 10:39 PM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Critical Strip
Hello, everyone! Here's a nice property of zeta function; I would like to present it as an exercise : Prove that Balarka . 
November 13th, 2012, 12:09 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Critical Strip
Hint : consider the difference and make N =Im[s].

November 13th, 2012, 02:59 PM  #3 
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16  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 . 
December 28th, 2012, 11:13 PM  #4  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Critical Strip Quote:
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  
December 29th, 2012, 04:40 AM  #5 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Re: Critical Strip
WELCOME BACK! 

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