# Tagged Questions

This tag is used if a reference is needed in a paper or textbook on a specific result.

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### a continuous analogue of a graph theory question

I am reading a paper and it mentions a continuous analogue of a related graph theory question that people concern. The question is that suppose $E\subset Q=[0,1]^2$ has lebesgue measure $|E|>0$, is ...
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### Unreasonable application of mathematics to the other areas [on hold]

What are some papers or talks on the philosophy of mathematics which contains some statements about the unnecessary and unreasonable application of mathematics in other areas of science? I found ...
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### Is there any good survey on the hook length formula and related topics?

I am recently doing some research related to the hook length formula. The hook formula counts the number of Young tableaux of certain type. I find there are plenty of research already been done and ...
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### Simultaneous extension of modules

Let $R$ be a commutative ring. Suppose $R$-modules $X,A,B,C$ and $Y$ are given such that the outer two rows and the outer two columns in the following diagram are exact. $\hskip1in$ Does it ...
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### Higher dimensional analogs of logarithmic density

For a set $A\subseteq \mathbb{N}$ its lower/upper asymptotic/logarithmic densities are given by \begin{align*} \underline{d}(A)=\liminf_{N\to\infty} \frac{|A\cap [1,N]|}{N},\\ \bar{d}(A)=\limsup_{N\to\...
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### Nonabelian $H^2$ and Galois descent

I would like to know whether the following metatheorem on nonabelian $H^2$ has been ever stated and/or proved. Let $k$ be a perfect field and $k^s$ its fixed separable closure. Let $X^s$ be a variety ...
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### Triangulation in which every Triangle has at least one Boundary edge

I am looking for information about Triangulation of a bounded (polygonal) planar region in which every triangle has at least one Boundary edge, that is every triangle has at least one edge which is ...
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### Reference: Finsler Derivative?

On the wikipedia page "Generalizations of derivative" the author mentions: " in Finsler geometry, one studies spaces which look locally like Banach spaces. Thus one might want a derivative with some ...
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### Reference for nonlinearity of covers of $\operatorname{SL}(2,\mathbb R)$

It is known that no nontrivial connected cover of $\operatorname{SL}(2,\mathbb R)$ admits a faithful finite dimensional linear representation (see, for example, page 143 in Fulton-Harris and Exercise ...
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### Interplay between the Cayley graph of a finite group and its realizability over Q

As the structure of any finitely generated, and thus any finite, group, can be described by its Cayley graph, have partial results on the realizability of such a group over $Q$ been obtained ...
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### Reference request - Jacquet module and asymptotic of matrix coefficients

Hello, I would like to know some nice references about the relation between asymptotics of matrix coefficients of representations of reductive groups over local fields, and the pairing between the ...
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### Fermat-Wiles “first case” in extensions of cyclotomic fields

I fell on the following fact : Let $p$ be an odd prime, let $K$ denote the $p$-th cyclotomic field, let $L$ be an extension of $K$ with finite degree not divisible by $p,$ and assume that the prime ...
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### What is know about maps between loop spaces of Spheres? - Reference request

What is know in general about the maps $\Omega^rS^n\rightarrow\Omega^sS^m$ between loop spaces of Spheres, or, perhaps to phrase it better, the groups $[\Omega^rS^n,\Omega^sS^m]$ for various values ...
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### Reference for holder estimate on parabolic equation with neumann boundary condition

I saw a type of holder estimate in Friedman's book: partial differential equations of parabolic type(page 200 3.24) as following: Suppose we have a uniformly parabolic equation with holder ...
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### Jacobi's theorem on sums of two squares (reference request)

One of Jacobi's theorems states that the number of representations of a positive integer $n$ as a sum of two squares of integers equals $$4(d_1(n)-d_3(n)),$$ where the function $d_i$ counts the number ...
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### DG categories in algebraic geometry - guide to the literature?

Although my experience with DG categories is pretty basic I find them to be a very neat tool for organizing (co-)homological techniques in algebraic geometry. For someone who has algebro-geometric ...
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### Combination of certain linear-programming topics new?

Consider the combination of the following topics, aimed at a future book on Linear Programming: Generalization of certain parts of the polyhedron theory and of the Simplex Algorithm to arbitrary ...
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### Existence of flat connections via characteristic classes, for nice groups

I have two questions about what I write below (which honestly seems pretty elementary). Is it true (more or less)? Is there a clean reference that I can cite. Let $G$ be a compact Lie group, $M$ a ...
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### Reference Request: $M_t/M_t/1/K$ queue length distributions

I am investigating functionals defined over sequences of discrete probability distributions related to dynamical/stochastic system performance. As an initial step, I am searching for references that ...
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### Does anyone have Delzell's Thesis on Bad Points of Forms?

Since a number of papers (e.g. this one) treating denominators in Hilbert's 17th problem point to E.G. Strauss's unpublished letter to G. Kriesel or to Chapter 5 of Delzell's Thesis, which contains an ...
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### Zeros of polynomials modulo a non-prime

Suppose I have a set $S$ and I want to find a polynomial $p$ such that $p(s) = 0 \mod n$ if $s \in S$, and that it is non-zero modulo $n$ otherwise. In the literature such an $S$ is sometimes called ...
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### Homotopical interpretation of flatness?

I have read a discussion (in a less common language) which discussed a homotopical interpretation of flatness, which went something like: A map of commutative algebras is flat if pushing it out ...
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### Critical points in $ZF$ without Choice

Recall the definition of critical point for set theory: A critical point of an elementary embedding of one transitive class into another transitive class is the smallest ordinal not mapped to ...
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### Laplace transform (or characteristic functional) of atomic random measure

A random (nonnegative Radon) measure $M$ (on $\mathbb R^n$, say) has its law characterized by the Laplace transform $\mathbb E\exp(-\int \varphi(x)\ M(dx))$, $\varphi\in C_c^+(\mathbb R^n)$ (...
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### Reference or counter-example for Closed Graph Theorem for multivalued maps in general topological spaces

Could someone be so kind to point me in the direction of a citeable proof of the following version of the Closed Graph Theorem? (i.e. assuming this is true, could someone give me a literature ...
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### $H^1$-continuity of Laplace's equation with respect to boundary data

Let $\Omega\subset \mathbb{R}^d$ be open and bounded with $C^\infty$ boundary $\partial\Omega$, $\phi\colon \partial\Omega \rightarrow \mathbb{R}$ continuous and $u^\phi$ the solution to Laplace's ...
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### Reference request: Bounding exponential sum $\sum_{x \in [0,X]} \Lambda(x) e(\beta_d x^d + \ldots + \beta_1 x )$

Let $1 \leq i \leq d$, $q \in \mathbb{N}$, and $0 \leq a_{i} < q$. Let $$\mathfrak{M}^{(i)}_{a_{ i}, q} (C) =\{ \beta_{i} \in [0,1) : | \beta_{i} - a_{i}/q | \leq (\log X)^{C} X^{-i} \} .$$ We ...
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### Coefficients in expansion of a classical symmetric polynomial

If we expand $$P_3(x_1,\ldots, x_n):=\Pi_{1\leq i<j<k\leq n} (x_i+x_j+x_k),$$ then P_3 = \sum_\alpha \sum_{\mathcal{O}(\alpha)} c_\alpha x_1^{\...
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