From ad16c1eb532fb068ebea6837b13b0cff372b000e 2017-09-10 16:12:37
From: András Gilyén <gilyen@cwi.nl>
Date: 2017-09-10 16:12:37
Subject: [PATCH] counter examplegit pull

---

diff --git a/main.tex b/main.tex
index 4f050f48beeb07256a19c6dde8c0bdee9ca9ed90..eb277bc599cce218edf263cf67e5589dbb49819e 100644
--- a/main.tex
+++ b/main.tex
@@ -180,6 +180,7 @@
   		\item $\exists p_c=\lim\limits_{k\rightarrow\infty}1\left/\sqrt[k]{a_{k}^{(k+1)}}\right.$ \label{it:lim}			
 	\end{enumerate}
 	\colorbox{red}{\ref{it:pos}-\ref{it:geq} is false since $a_{1114}^{(10)}<0$ -- needs to be double checked!}
+	I figured this out by observing that $R^{(10)}(p)$ has a pole inside the disk of radius $0.96$. This also means that $R^{(10)}(p)=\sum_{k=0}^{\infty}a_k^{(10)}p^k$ is only true in an analytic sense, since for $p>0.96$ the right hand side does not converge.
 	
 	We also conjecture that $p_c\approx0.61$, see Figure~\ref{fig:coeffs_conv_radius}.