# Questions tagged [reference-request]

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

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

13,375
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This was originally posted on math.stackexchange as https://math.stackexchange.com/questions/4589793, where I was suggested to move it here.
I'm searching a lecture note by C. Skinner named "...

2
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1
answer

556
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Undoubtedly one of the news that attracted the most attention this year was the result of Yitang zhang on the Landau-Siegel zeros.
Since it is not possible to be attentive to great results in all ...

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I want to learn "Topology of Space of Holomorphic Functions" in a rigorous way. Please advise me some references. My interest arose in this topic of Complex Analysis from the following ...

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Let $G$ be a group. Denote by $\mathrm{Z}(G)$ and $G'$ the center of $G$ and the derived subgroup of $G$, respectively. Assume $G'\subseteq\mathrm{Z}(G)$. Then, it is clear that $G$ is a nilpotent ...

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I'm just looking for references in the literature for some observations I made for fun about the Collatz conjecture.
The Collatz conjecture states that any positive integer $n$ can eventually be ...

4
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91
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Does anyone have a go-to reference for a proof of the Jewett–Krieger theorem in dynamical systems/ergodic theory? It's quite technical and I'd like to have something to show students. The best I ...

3
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I am studying spaces of the form $C^{k}(\mathcal{M},\mathcal{N})$ between manifolds ($k=\infty$ allowed) and I am looking for extensive references, especially analysing their topology and smooth ...

2
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42
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My question pertains eigenvectors of matrices with somewhat evenly distributed entries.
Let $M$ be an $N \times N$ matrix with complex entries (think of $N$ as a large integer). You can assume that $M$...

3
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The following result was originally proven by Engelking in his 1969 paper On closed images of the space of irrationals (AMS, JSTOR, MR239571, Zbl 0177.25501)
Every Polish space (i.e. every separable ...

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The monad version of the theorem at Topos of coalgebras over a comonad is as follows:
Let $\mathcal{E}$ be an (elementary) topos. Then if a monad $T : \mathcal{E} \rightarrow \mathcal{E}$ has a right ...

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+300

Let $D$ be a Weil divisor on a normal toric variety $X$ with fan $\Sigma$ that is invariant under the action by the torus $T$. Then Proposition 4.3.2 of the textbook Toric Varieties by Cox, Little and ...

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In the proof of Lemma 2.1 in
Ershov, Mikhail; He, Sue, On finiteness properties of the Johnson filtrations, ZBL06904638,
the authors claim the following (without proof).
Let $G$ be a finitely ...

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55
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For years umbral calculus have fascinated me. Bernoulli numbers (which represent powers of Bernoulli umbra) are involved in many classic power series expansions.
Yet, it still remains mistery what ...

2
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Given a simple graph $G=(V,E)$, we can consider matchings, $M\subseteq E$,
where $M$ is a matching iff no vertex is shared between different edges.
The number of edges in $M$ is denoted $|M|$.
The ...

5
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1
answer

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$\DeclareMathOperator\PSL{PSL}\DeclareMathOperator\Aut{Aut}\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\GL{GL}$I am looking to classify the homomorphisms from the group $\PSL(2,p)=\Aut(\mathbb{P}^...

3
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(This is in part a request for references and in part a somewhat pedagogical question.)
I gave a course on expanders seven years ago, and I am giving a course on expanders again now. We will soon do ...

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92
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While working on an abstract problem, I came up with the following question:
Let $\Omega_1 := \mathrm B(-1, 1)$ and $\Omega_2 := \mathrm B(1, 1)$, where $\mathrm B(x, r) \subseteq \mathbb R^2$ denotes ...

2
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1
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68
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I need to find the following paper:
“K. Urbanik and WA Woyczynski, A random integral and Orlicz spaces, Bulletin de l'Académie Polonaise des Sciences, Série des sciences mathématiques, astronomiques ...

4
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If you could recommend a few papers for someone entering derived algebraic geometry outside of the classical category theory, algebraic geometry, and algebraic topology sequences? What would they be?

6
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Over a field $ k $ of characteristic zero, actions of $ \widehat{\mathbb{G}_{a}} $ on a variety $ \operatorname{Spec}(A) $ are obtained from $ A $-derivations $ \delta $ of $ A $ over $ k $ via the co-...

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Let $W$ be the adjacency matrix of a directed graph. Let us denote by $D$ the associated in-degree matrix, whose diagonal entries are given by $D_{ii} = \sum_j W_{ij}$. The associated Laplacian
$$ L =...

2
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If $f: X \to S$ is a proper map from a complex manifold to a disc, $Y=f^{-1}(0)$ is a divisor with strictly normal crossings and the action of monodromy on $X_t=f^{-1}(t)$ for some (hence any) $t \neq ...

4
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I suppose that what I look for is known, but I can't find it.
Let $\left\lbrace I_n=[a_n,b_n)\right\rbrace$ and $\left\lbrace J_n=[b_n,c]\right\rbrace$ ($n\in\mathbb{N}$) be two countable families of ...

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Consider the nonparametric varying coefficient model
$$y_i = x_i'\beta(z_i)+e_i,$$
where $(x_i, z_i)$ are covariates on $[0,1]^m\times [0,1]^k$, $e_i$ are the errors, and $\beta:[0,1]^k\to [0,1]^m$ is ...

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514
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Is there a name/reference for the following object? We have a vector space $V$ over some field with two associative bilinear operations $\circ,*:V \times V \to V$ which satisfy the interchange law, i....

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Let $\Omega = [0, 1]^d$ and suppose that $f \colon \Omega \to \mathbb{R}$ lies in order $m > d/2$ Sobolev space; i.e.,
$$
\|f\|_{H^m(\Omega)}^2 = \sum_{|\alpha| \leq m} \|D^\alpha f\|_{L^2(\Omega)}^...

5
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I have been studying $3$-manifolds recently and I got stuck in the following situation. For lens spaces the below fact is true.
Let $G$ be a finite group acting freely and orthogonally on $S^3$ so ...

9
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1
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581
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Let $^na$ denote the $n$th tetration of $a$, so that $^0a=1$ and
$$^{n+1}a=a^{^na}$$
for $n=0,1,\dots$. (For complex $x$ and $y$, here we use the definition $x^y:=e^{y\ln x}$, where $\ln$ is the ...

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0
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37
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I know the following theorems due to Rogers. Let $X$ denote the space of $n$-dimensional unimodualar lattices in $\mathbb R^n$, equipped with the canonical Haar measure.
Theorem 1(Siegel-Rogers). Let ...

12
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1
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250
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Are there models of ZFC in which $\mathfrak{r}$ is strictly less than $\mathfrak{s}$? I've not been able to find any forcings that end up with this result.
Here $\mathfrak{r}$ is the reaping number $\...

4
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1
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$\newcommand\B{\mathscr B}\newcommand\A{\mathscr A}\newcommand\si{\sigma}$Let $I:=[0,1]$, and let $\B$ and $\B^2$ denote the Borel $\si$-algebras over $I$ and $I^2$, respectively. Let $\A$ stand for ...

2
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1
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Matrices with entries in the finite field of two elements $\mathbb{F}_2$, and with the usual operations of matrix addition and multiplication, have been intensively studied, especially due to their ...

6
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2
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I'm a PhD student in category theory, more specifically I study 2-dimensional category theory, that means bicategories, pseudofunctors, careful definitions of various structures you can put on this ...

3
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Kechris in his Classical Descriptive Set Theory book gives the following definition (Definition 24.1) and characterization (Theorem 24.15) of Baire class $1$ functions:
Definition. Let $X,Y$ be ...

9
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1
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It is well known that the principal block $\mathcal{O}_0$ of the BGG category $\mathcal{O}$ of a semisimple Lie algebra is equivalent to the category of finitely generated modules over a certain ...

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In a survey article Algebraic geometry in mixed characteristic, B. Bhatt writes
For instance, given a commutative ring $R$ with a finitely generated ideal $I$,
the assignment carrying $R$ to the $\...

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2
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Let $X,Y$ be two $n\times n$ i.i.d. Gaussian matrices (entries are i.i.d N(0,1) and $X$ and $Y$ are independent).
Consider their product normalized by the standard variance of entries $\frac{XY}{\sqrt ...

3
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1
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I am interested in knowing more about applications of Young diagrams and Young tableaux to Quantum Mechanics. A friend of mine suggested as a reference the following book:
Wybourne, B.G.; "...

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I'm looking for a reference that covers things like the lemma below - it doesn't have to be the exact statement I'm going to give, anything in the general ballpark would probably be useful. Or if you ...

4
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Let $X,Y$ be metric spaces. Let $f,g : X \to Y$ be two maps and $x_0 \in X$. Let us say that $f$ and $g$ are tangent at $x_0$ if the following condition is satisfied: For every $\epsilon > 0$ there ...

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Alot is known about the (non)-displaceability of the fibers of a toric symplectic manifold. For example there is Mcduff's method of probes to prove displaceability results using the moment polytope, ...

3
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$\DeclareMathOperator\SU{SU}\DeclareMathOperator\PSL{PSL}$I am self-studying triangle groups and the following question comes up.
Let $G$ denotes $(2,3,7)$ triangle group. It is symmetry group of $(2,...

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For a given integer $n$, I am interested in the number of different numerical semigroups one can make with a generating set consisting only of integers in $[n]$.
I have done some small examples. For $...

2
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147
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There are some nice connections between properties of sets and properties of their characteristic functions.
For instance:
a set $C\subset \mathbb{R}$ is closed (resp. open) IFF the characteristic ...

2
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1
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165
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Is there a simple proof that there is no Anosov flow on $S^2$? Where can I find it?

4
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I am looking for a modern, maybe shorter or even easier, reference for Theorem II of Homogeneous vector bundles (R. Bott, Annals of mathematics, 1957). This is a theorem where the Dolbeault cohomology ...

4
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2
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In the setting of symbolic dynamics over $\mathbb{Z}^d$, one can define for the $n$-th pattern complexity of a given a subshift $\Omega\subseteq \mathcal{A}^{\mathbb{Z}^d}$ as
$$ c_n(\Omega):= \Big\...

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1
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Let $(X, \Sigma, \mu)$ be a $\sigma$-finite complete measure space, $(E, |\cdot|)$ a Banach space, and $p \in (1, \infty)$. Let $L_p := L_p(X, \mu, E)$ be the Bochner space of all $\mu$-integrable ...

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Let $E$, $B$ be smooth manifolds, $\pi\colon E\to B$ be a smooth fiber bundle, and $h:B\to E$ be a smooth embedding. I would like to learn what is known about the following
Question. When does there ...

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1
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The following question is motivated from Chapter 2 (Generalized Hodge Systems in 2D), particularly Section 2.3 ($L^p$ theory for Hodge systems in 2D) of Christodoulou and Klainerman's book, The global ...