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May 4th, 2013, 02:45 AM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Transcendence of Gelfond'slike Constants
Can it be proved whether for is transcendental or not? It doesn't seem that it can be deduced from any known results; even I think it can't be proved conditionally using the current conjectures on transcendence theory. Balarka . 
May 7th, 2013, 10:21 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Transcendence of Gelfond'slike Constants
Anyone?

May 7th, 2013, 01:34 PM  #3 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26  Re: Transcendence of Gelfond'slike Constants
I only wish I could even pretend to understand the question.

May 7th, 2013, 02:04 PM  #4  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Transcendence of Gelfond'slike Constants Quote:
 
May 7th, 2013, 02:09 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Transcendence of Gelfond'slike Constants Quote:
I don't think that the question can be answered at present.  
May 7th, 2013, 09:18 PM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Transcendence of Gelfond'slike Constants Quote:
 
May 8th, 2013, 05:16 AM  #7  
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26  Re: Transcendence of Gelfond'slike Constants Quote:
 
May 8th, 2013, 05:37 AM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Transcendence of Gelfond'slike Constants Quote:
There are numbers we know not to be algebraic, like e. We call such numbers "transcendental". As it happens we know that e^Pi is also transcendental. The question is whether we can extend the proof that e^Pi is transcendental to numbers of the form e^(Pi + a) for a rational, or else find a different proof that such a number is transcendental. I don't know but suspect this is beyond current capabilities.  
May 8th, 2013, 06:00 AM  #9 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Transcendence of Gelfond'slike Constants
Yes, I was quite surprised when I first found out that some irrationals behave in certain significant ways the way rationals do and unlike the way certain other fellow irrationals do. Are there any other significant subdivisions of irrationals like this algebraic vs transcendental distinction? 
May 8th, 2013, 09:07 AM  #10  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Transcendence of Gelfond'slike Constants Quote:
Quote:
Quote:
What is the irrationality measure of exp(Pi+a) for rational a? Forget the a, what is the irrationality measure for exp(Pi) ?  

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constants, gelfondlike, transcendence 
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