We consider a discretization of the Laplace operator on $\mathbb Z^2$, https://en.wikipedia.org/wiki/Discrete_Laplace_operator
Then, it is natural to consider its fundamental solution $u$, i.e. $|u(x)|\leq C \ln|x|,\Delta u = 1$ at $(0,0)$ and $\Delta u=0$ elsewhere. I am sure that somewhere it ...
While reading several articles about lattice basis reduction I am left with a few questions.
For one, I came across this piece of text
Let $\alpha$ and $\beta \in \mathbb{R}$. Also let $X>0$ and $X$ is large. Then to compute $x,y \in \mathbb{Z}$ with $\text{max} (|x|,|y|) \le X$ and such that $...
@MartinSleziak the tag graph-theory is clearly missing there (and is virtually top-level). In case of an edit, removing the capital from "Discrete" would be useful.
@MartinSleziak I think that we can consider mg.metric-geometry as the standard top-level tag for all questions about Euclidean lattices, so it would be a perfect replacement here.
@MartinSleziak Now I noticed that this was already mentioned in a comment.
Dear @Gil Kalai: I fixed the hyperlinks in this answer. Also, it should be noted that all the links other than the blog posts require an AMS subscription. — Ricardo AndradeNov 10 '13 at 10:44
specific-question I have removed the deprecated here - still I am not sure which other tags should be used for that question: Expanding the square of sum. ( I am not sure whether the question is suitable for MO, either.)
If there any way to expand the following?
$$\left(\sum_{i=1}^nx_i\right)^{\frac{1}{2}}$$
and more generally, a way to expand
$$\left(\sum_{i=1}^nx_i\right)^{\frac{p}{q}}$$
where $\gcd(p,q) = 1$
More closed to my original problem, is there any formula for:
$$\left(\sum_{i=1}^nx_i\right)^{\fra...
While reading several articles about lattice basis reduction I am left with a few questions.
For one, I came across this piece of text
Let $\alpha$ and $\beta \in \mathbb{R}$. Also let $X>0$ and $X$ is large. Then to compute $x,y \in \mathbb{Z}$ with $\text{max} (|x|,|y|) \le X$ and such that $...
If there any way to expand the following?
$$\left(\sum_{i=1}^nx_i\right)^{\frac{1}{2}}$$
and more generally, a way to expand
$$\left(\sum_{i=1}^nx_i\right)^{\frac{p}{q}}$$
where $\gcd(p,q) = 1$
More closed to my original problem, is there any formula for:
$$\left(\sum_{i=1}^nx_i\right)^{\fra...
