I want to study the structure of the rig of L-functions $\mathcal{M}$, which is defined as the maximal set of automorphic L-functions of $\mathrm{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ for some $n$ that be closed under the usual product and the tensor product corresponding to the Rankin-Selberg convol...
let $L=\mathbb{Q}(\sqrt[5]{n},\zeta_5)$ and $K=\mathbb{Q}(\zeta_5)$ the $5^{th}$ cyclotomic fields, we now that $[L:K] = 5$ and $ GAl(L/K) =\langle\sigma\rangle$ so we call $\mathcal{A}$ an ambigous ideal class of the extension $L/K$ if and only if $\mathcal{A}^{\sigma}= \mathcal{A}$. My questi...
Let $B_1$ and $B_2$ be two balls with the same radius, in $\mathbb R^n$ with the $\ell^1$ norm. The distance between the centers of $B_1$ and $B_2$ is $d(B_1, B_2)$. Is there any deterministic method or probabilistic method to calculate the minimum volume of $B_1 \cap B_2$?
Given a finite set of convex $d$-dimensional polytopes $\mathcal P$, for some $d\ge 2$. Question: Is it true that there are only finitely many different convex $(d+1)$-dimensional polytopes whose facets are solely (scaled and rotated versions of) polytopes in $\mathcal P$? Some clarificat...
Let $B_1$ and $B_2$ be two balls with the same radius, in $\mathbb R^n$ with the $\ell^1$ norm. The distance between the centers of $B_1$ and $B_2$ is $d(B_1, B_2)$. Is there any deterministic method or probabilistic method to calculate the minimum volume of $B_1 \cap B_2$?
Ok, so I try to formulate rigorously the question in the title, for which I am asking for references. My definitions may be flawed, so feel free to adjust/correct them! I care about dimensions 2 and 3 below, but feel free to mention general d as well. Let $d\ge 1$ be an integer, $G=(V,E)$ be a g...
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