Comments on: Hilbert’s seventh problem, and powers of 2 and 3
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoWed, 10 Oct 2018 19:15:38 +0000
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By: seaneberhard
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-505895
Wed, 10 Oct 2018 17:07:44 +0000http://terrytao.wordpress.com/?p=5072#comment-505895 Typo: the inequality in the first display after Prop 7 goes the wrong way.

[Corrected, thanks – T.]

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By: Gottfried Helms
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-485957
Thu, 07 Sep 2017 12:49:12 +0000http://terrytao.wordpress.com/?p=5072#comment-485957I improved my rough guess to $c=0.005,C=1.01$ See some pictures which are that guesses basis at https://math.stackexchange.com/q/2418882/1714 I plotted up to $p=1e175$
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By: Gottfried Helms
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-485950
Thu, 07 Sep 2017 07:57:32 +0000http://terrytao.wordpress.com/?p=5072#comment-485950… sorry, meant to cite you as “…c,C>0…”
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By: Gottfried Helms
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-485949
Thu, 07 Sep 2017 07:56:18 +0000http://terrytao.wordpress.com/?p=5072#comment-485949In corollary 4 you write, “…for effectively computable constants c,C>1 …” . So far I’ve no idea how I could compute values for such constants; based on plotting up to p=1e125 it seems c=0.01, C=1 the separation is larger than the formula on the rhs – but this is surely only a guess. Are that constants already computed somewhere?
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By: Israel Aku
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-482407
Wed, 14 Jun 2017 07:33:47 +0000http://terrytao.wordpress.com/?p=5072#comment-482407Hello Terry, is there a case where a is algebraic and b is transcendental, and the value of a^b is algebraic? I very much enjoyed the banner’s quote. Is it from Emma Lazarus’ The New Colossus as a standalone poem or as an inscription on the Statue of Liberty?

[One can take for instance and . -T.]

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By: Anonymous
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-451235
Fri, 30 Jan 2015 14:22:45 +0000http://terrytao.wordpress.com/?p=5072#comment-451235

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By: Ben
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-451230
Fri, 30 Jan 2015 10:02:27 +0000http://terrytao.wordpress.com/?p=5072#comment-451230Do it again. Wouaow. What a synthesis ! Just a naive question. As \displaystyle |3^p – 2^q| \geq 1, for which For which p,q does the equality holds ? I know of 1,2. Are there other solutions ? Thanks.
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By: Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory | What's new
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-249017
Fri, 25 Oct 2013 15:48:15 +0000http://terrytao.wordpress.com/?p=5072#comment-249017[…] used independently many times in mathematics; for instance, it plays a key role in the proof of Baker’s theorem in transcendence theory, or Stepanov’s method in giving an elementary proof of the Riemann hypothesis for finite […]
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By: Eleventh Linkfest
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-161715
Tue, 21 Aug 2012 18:07:07 +0000http://terrytao.wordpress.com/?p=5072#comment-161715[…] Terence Tao: A geometric proof of the impossibility of angle trisection by straightedge and compass, Hilbert’s seventh problem, and powers of 2 and 3 […]
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By: mathsetc
https://terrytao.wordpress.com/2011/08/21/hilberts-seventh-problem-and-powers-of-2-and-3/#comment-90162
Fri, 07 Oct 2011 00:56:18 +0000http://terrytao.wordpress.com/?p=5072#comment-90162[…] Hilbert’s seventh problem, and powers of 2 and 3 (terrytao.wordpress.com) […]
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