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 <title>Open Problem Garden - Schanuel&amp;#039;s Conjecture - Comments</title>
 <link>http://openproblemgarden.org/op/schanuels_conjecture</link>
 <description>Comments for &quot;Schanuel&#039;s Conjecture&quot;</description>
 <language>en</language>
<item>
 <title>Re: I must agree with the  (re: Schanuel&#039;s Conjecture)</title>
 <link>http://openproblemgarden.org/op/schanuels_conjecture#comment-6708</link>
 <description>&lt;p&gt;Encouraged by the previous comments, I changed the rating of this problem and the &quot;mimic&quot; one. Thanks for the feedback. &lt;/p&gt;
</description>
 <pubDate>Mon, 18 Jan 2010 23:22:11 +0100</pubDate>
 <dc:creator>Robert Samal</dc:creator>
 <guid isPermaLink="false">comment 6708 at http://openproblemgarden.org</guid>
</item>
<item>
 <title>I must agree with the  (re: Schanuel&#039;s Conjecture)</title>
 <link>http://openproblemgarden.org/op/schanuels_conjecture#comment-6707</link>
 <description>&lt;p&gt;I must agree with the previous comment. Schanuel&#039;s conjecture is likely the most important open problem in Transcendental Number Theory. I realize that this might not be as major a field as the study of &quot;mimic&quot; numbers, but.....&lt;/p&gt;
</description>
 <pubDate>Mon, 18 Jan 2010 18:10:32 +0100</pubDate>
 <dc:creator>Anonymous</dc:creator>
 <guid isPermaLink="false">comment 6707 at http://openproblemgarden.org</guid>
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<item>
 <title>from Gasses  (re: Schanuel&#039;s Conjecture)</title>
 <link>http://openproblemgarden.org/op/schanuels_conjecture#comment-6699</link>
 <description>&lt;p&gt;I am just curious why &#039;importance&#039; is given as 2 stars when (according to wikipedia) &quot;The conjecture, if proven, would subsume most known results in transcendental number theory.&quot; Some of these results include results on this page that have greater importance than 2 stars.&lt;/p&gt;
</description>
 <pubDate>Sun, 27 Dec 2009 07:18:50 +0100</pubDate>
 <dc:creator>Anonymous</dc:creator>
 <guid isPermaLink="false">comment 6699 at http://openproblemgarden.org</guid>
</item>
<item>
 <title>Schanuel&#039;s Conjecture</title>
 <link>http://openproblemgarden.org/op/schanuels_conjecture</link>
 <description>&lt;table cellspacing=&quot;10&quot;&gt;
&lt;tr&gt;
  &lt;td&gt;
    Author(s):
        &lt;a href=&quot;/category/schanuel_stephen&quot;&gt;Schanuel&lt;/a&gt;&amp;nbsp;&amp;nbsp;
  &lt;/td&gt;
  &lt;td align=right&gt;
    Subject:
        &lt;a href=&quot;/category/number_theory_0&quot;&gt;Number Theory&lt;/a&gt; » &lt;a href=&quot;/category/analytic_number_theory&quot;&gt;Analytic N.T.&lt;/a&gt;&amp;nbsp;&amp;nbsp;
  &lt;/td&gt;
&lt;/tr&gt;

&lt;tr&gt;
  &lt;td colspan=2&gt;
    &lt;table border=1 cellspacing=&quot;5&quot;&gt;
      &lt;tr&gt;&lt;td&gt;
        &lt;div class=&quot;envtheorem&quot;&gt;&lt;b&gt;Conjecture&lt;/b&gt;&amp;nbsp;&amp;nbsp; Given any &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png&quot; alt=&quot;$ n $&quot; /&gt; complex numbers &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/b7779accf6429c04a1809e479068a39e57552d59.png&quot; alt=&quot;$ z_1,...,z_n $&quot; /&gt; which are linearly independent over the rational numbers &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/f360db0eb889cd59a651c1e7b4bc99fc86f6ee6c.png&quot; alt=&quot;$ \mathbb{Q} $&quot; /&gt;, then the extension field &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/08d62d0ffdaba5b8acbe2a1e75839421fc8ac633.png&quot; alt=&quot;$ \mathbb{Q}(z_1,...,z_n,\exp(z_1),...,\exp(z_n)) $&quot; /&gt; has transcendence degree of at least &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png&quot; alt=&quot;$ n $&quot; /&gt; over &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/f360db0eb889cd59a651c1e7b4bc99fc86f6ee6c.png&quot; alt=&quot;$ \mathbb{Q} $&quot; /&gt;. &lt;/div&gt;

      &lt;/tr&gt;&lt;/td&gt;
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  &lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;</description>
 <category domain="http://openproblemgarden.org/category/schanuel_stephen">Schanuel, Stephen</category>
 <category domain="http://openproblemgarden.org/category/algebraic_independence">algebraic independence</category>
 <category domain="http://openproblemgarden.org/category/number_theory_0">Number Theory</category>
 <category domain="http://openproblemgarden.org/category/analytic_number_theory">Analytic Number Theory</category>
 <comments>http://openproblemgarden.org/op/schanuels_conjecture#comment</comments>
 <pubDate>Tue, 08 Jul 2008 14:41:20 +0200</pubDate>
 <dc:creator>Charles</dc:creator>
 <guid isPermaLink="false">1788 at http://openproblemgarden.org</guid>
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