<story><title>The Riemann Hypothesis, explained</title><url>https://medium.com/@JorgenVeisdal/the-riemann-hypothesis-explained-fa01c1f75d3f#.9hp0wrml3</url></story><parent_chain></parent_chain><comment><author>tzs</author><text>There are some interesting statements that are equivalent to the Riemann Hypothesis. What &amp;quot;equivalent&amp;quot; means is that if the statement is true then RH must be true, and if RH is true then the statement must be true.&lt;p&gt;Here&amp;#x27;s one I find particularly nice.&lt;p&gt;Let s(n) = the sum of the divisors of n, for a positive integer n. For example s(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28.&lt;p&gt;Let H(n) = 1 + 1&amp;#x2F;2 + 1&amp;#x2F;3 + ... + 1&amp;#x2F;n.&lt;p&gt;The RH is equivalent to the claim that for every integer n &amp;gt;= 1:&lt;p&gt;s(n) &amp;lt;= H(n) + exp(H(n)) log(H(n))&lt;p&gt;This is due to Jeffry C. Lagarias. Here&amp;#x27;s his paper showing the equivalence: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;math&amp;#x2F;0008177&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;math&amp;#x2F;0008177&lt;/a&gt;</text></comment>
<story><title>The Riemann Hypothesis, explained</title><url>https://medium.com/@JorgenVeisdal/the-riemann-hypothesis-explained-fa01c1f75d3f#.9hp0wrml3</url></story><parent_chain></parent_chain><comment><author>williamstein</author><text>Shameless promotion: I published a book recently trying to explain RH, and my coauthor gave a great talk about it, which is here: &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;wstein.org&amp;#x2F;rh&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;wstein.org&amp;#x2F;rh&lt;/a&gt;</text></comment>