• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 Universal uniqueness criterion? bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 07/06/2009, 08:56 AM (This post was last modified: 07/06/2009, 09:01 AM by bo198214.) (07/06/2009, 12:53 AM)BenStandeven Wrote: the path would have to pass through a point with imaginary value 2 pi, and also through its conjugate. Then the other side of the region would intersect itself at the exponential of that point. Say the curve $\gamma: [0,1]\to \mathbb{C}$ is injective and connects two points $\gamma(0)=a$ and $\gamma(1)=b$ with equal real part and with $\Im(b)-\Im(a)>2\pi$. One needs to show that then there is always a pair of points $c_1=\gamma(t_1)$ and $c_2=\gamma(t_2)$ with equal real part and with $\Im(c_2)-\Im(c_1)=2\pi$. This sounds very plausible but I couldnt prove it except for certain simple shapes of $\gamma$, e.g. convex. « Next Oldest | Next Newest »

 Messages In This Thread Universal uniqueness criterion? - by bo198214 - 05/21/2008, 06:24 PM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 05:19 AM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 06:42 AM RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 11:25 AM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 03:11 PM RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 05:55 PM RE: Universal uniqueness criterion? - by bo198214 - 05/23/2008, 12:07 PM RE: Universal uniqueness criterion? - by Gottfried - 06/25/2008, 06:15 AM Uniqueness of analytic tetration - by Kouznetsov - 09/30/2008, 07:58 AM RE: Uniqueness of analytic tetration - by bo198214 - 09/30/2008, 08:17 AM RE: Universal uniqueness criterion? - by bo198214 - 10/04/2008, 11:19 PM RE: Universal uniqueness criterion? - by Kouznetsov - 10/05/2008, 12:22 AM RE: Universal uniqueness criterion? - by Kouznetsov - 06/19/2009, 08:45 AM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 02:04 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 02:51 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 04:19 PM RE: miner error found in paper - by bo198214 - 06/19/2009, 04:53 PM i don't think it will work - by Base-Acid Tetration - 06/19/2009, 05:17 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 06:25 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 06:27 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 07:59 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/20/2009, 02:01 PM RE: Universal uniqueness criterion? - by bo198214 - 06/20/2009, 02:10 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 02:39 PM RE: Universal uniqueness criterion? - by Kouznetsov - 06/23/2009, 05:46 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 09:28 PM RE: Universal uniqueness criterion? - by Kouznetsov - 06/24/2009, 05:02 AM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 07/04/2009, 11:17 PM RE: Universal uniqueness criterion? - by Kouznetsov - 07/05/2009, 08:28 AM RE: Universal uniqueness criterion? - by bo198214 - 07/05/2009, 06:54 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Semi-exp and the geometric derivative. A criterion. tommy1729 0 1,698 09/19/2017, 09:45 PM Last Post: tommy1729 A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 14,247 02/17/2017, 05:21 AM Last Post: JmsNxn Uniqueness of half-iterate of exp(x) ? tommy1729 14 18,686 01/09/2017, 02:41 AM Last Post: Gottfried Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,913 03/19/2016, 10:44 AM Last Post: fivexthethird [2014] Uniqueness of periodic superfunction tommy1729 0 2,304 11/09/2014, 10:20 PM Last Post: tommy1729 Real-analytic tetration uniqueness criterion? mike3 25 26,093 06/15/2014, 10:17 PM Last Post: tommy1729 exp^[1/2](x) uniqueness from 2sinh ? tommy1729 1 2,720 06/03/2014, 09:58 PM Last Post: tommy1729 Uniqueness Criterion for Tetration jaydfox 9 12,927 05/01/2014, 10:21 PM Last Post: tommy1729 Uniqueness of Ansus' extended sum superfunction bo198214 4 7,772 10/25/2013, 11:27 PM Last Post: tommy1729 A question concerning uniqueness JmsNxn 3 6,482 10/06/2011, 04:32 AM Last Post: sheldonison

Users browsing this thread: 1 Guest(s)