Corrections David

sec-lattices.tex

@@ -44,7 +44,7 @@ In the following, we work with $q$-ary lattices, for some prime number $q$, defi
   For a lattice~$\Lambda$, a vector $\mathbf{c} \in \RR^n$ and a real~$\sigma>0$, define the distribution function
   $\rho_{\sigma,\mathbf{c}}(\mathbf{x}) \triangleq \exp(-\pi\|\mathbf{x}- \mathbf{c} \|^2/\sigma^2)$.
   The discrete Gaussian distribution of support~$\Lambda$, parameter~$\sigma$ and center $\mathbf{c}$ is defined as
-  $D_{\Lambda,\sigma,\mathbf{c}}(\mathbf{y}) = \rho_{\sigma,\mathbf{c}}(\mathbf{y})/\rho_{\sigma,\mathbf{c}}(\Lambda)$ for any $\mathbf{y} \in \Lambda$.
+  $D_{\Lambda,\sigma,\mathbf{c}}(\mathbf{y}) = \rho_{\sigma,\mathbf{c}}(\mathbf{y})/\rho_{\sigma,\mathbf{c}}(\Lambda)$ for any $\mathbf{y} \in \Lambda$, where $\rho_{\sigma, \mathbf{c}}(\Lambda) \triangleq \sum_{\mathbf x \in \Lambda} \rho_{\sigma, \mathbf{c}}(\mathbf{x})$.
   We denote by  $D_{\Lambda,\sigma}(\mathbf{y}) $ the distribution centered in $\mathbf{c}=\mathbf{0}$.
 \end{definition}