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Diffstat (limited to 'docs/nstrophy_doc/nstrophy_doc.tex')
| -rw-r--r-- | docs/nstrophy_doc/nstrophy_doc.tex | 4 |
1 files changed, 2 insertions, 2 deletions
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) |