My Math Forum Zeta on the critical line

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February 7th, 2013, 12:16 PM   #11
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Re: Zeta on the critical line

Quote:
 Originally Posted by mathbalarka I assumed it just by looking at the first few zeros of zeta : http://www.dtc.umn.edu/~odlyzko/zeta_tables/zeros1
Don't you think it is pretty weak for an argument to make such a conjecture? The important thing is to have an argument that specifies something about the integers.
Let me explain what I mean. I looked at the list and found always numbers with .00000 or .111111 or .222222 or .3333333.....999999 Now what should be special about .000000000 until infinity?? Why do you think more that there exists no zero with .00000000... than .6666666..... ??? If you can give me an argument on this then I would try to believe in Balarka's conjecture!!

February 7th, 2013, 09:16 PM   #12
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Re: Zeta on the critical line

Quote:
 Originally Posted by Dougy Don't you think it is pretty weak for an argument to make such a conjecture?
Yes, but we don't have anything strong in our hand except that list, do we?

Quote:
 Originally Posted by Dougy Now what should be special about .000000000 until infinity??
Nothing if we compare this to 0.6666 or 0.5555. But I also conjecture (call this Balarka's weak conjecture!) that there are no zeros of zeta with imaginary part a rational one. But for this to prove, we must prove the former one first.

Quote:
 Originally Posted by Dougy If you can give me an argument on this then I would try to believe in Balarka's conjecture!!
I think I have an argument but not the strongest one : there are no integral zeros of zeta on the half line because zeta is a transcendental function.

I got nothing more.

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