From 77043e249cf49fd533a1ffd6f53c0b6d6fcaaba8 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian@jauslin.org>
Date: Thu, 26 May 2022 20:54:30 -0400
Subject: Make N be the smallest power of 2 larger than 3*K+1

---
 docs/nstrophy_doc/nstrophy_doc.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'docs/nstrophy_doc/nstrophy_doc.tex')

diff --git a/docs/nstrophy_doc/nstrophy_doc.tex b/docs/nstrophy_doc/nstrophy_doc.tex
index 418520f..35c42ec 100644
--- a/docs/nstrophy_doc/nstrophy_doc.tex
+++ b/docs/nstrophy_doc/nstrophy_doc.tex
@@ -108,9 +108,9 @@ in which $\mathcal F^*$ is defined like $\mathcal F$ but with the opposite phase
 \end{equation}
 provided
 \begin{equation}
-  N_i>4K_i.
+  N_i>3K_i.
 \end{equation}
-Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q\in\mathcal K$, then $|p_i+q_i|\leqslant2K_i$.
+Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q,k\in\mathcal K$, then $|p_i+q_i-k_i|\leqslant3K_i$, so, as long as $N_i>3K_i$, then $(p_i+q_i-k_i)=0\%N_i$ implies $p_i+q_i=k_i$.
 Therefore,
 \begin{equation}
   T(\hat\varphi,k)
-- 
cgit v1.2.3-54-g00ecf

