# 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
questions

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A Fibonacci-type sequence is a sequence with two seed-values, $F_1$ and $F_2$, and which, for all $n>2$, abides by the recurrence relation $F_n = F_{n-1} + F_{n-2}$. If $F_1 = F_2 = s$, then the $n$...

2
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1
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59
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Given a general Banach space $B$ and a one-parameter family of contractions $F_t:B\to B$ which is defined for all $t \in (a,b)$. $F_t$ depends continuously on $t$ (in the sense $\lim_{\varepsilon\to 0}...

5
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139
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As far as I understand, the celebrated result of Kahn and Markovic about quasi-Fuchsian immersions of surfaces in hyperbolic 3-manifolds has the following corollary:
Let $M$ be a compact hyperbolic $3$...

13
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1
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385
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Equivariant homotopy theory focuses on spaces together with some group action on them. Jeroen van der Meer and Richard Wong have a paper where they use equivariant methods to compute the Picard group ...

5
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1
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222
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It is known that the number of ways to express $n \in \mathbb{Z}_{\geq 0}$ as a sum of three squares (let's denote it as $r_3(n)$) can be expressed as Hurwitz-Kronecker class number (certain weighted ...

5
votes

1
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264
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Let $M$ be a smooth manifold, $N\subset M$ be a smooth closed hypersurface not bounding a compact submanifold, and $X$ be a smooth nowhere-zero vector field on $M$. I would like to learn what is known ...

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0
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It has been known for long (Molloy and Reed 1995) that in a supercritical undirected configuration model, that is when $E[D(D-2)]>0$, $D$ degree of a uniform vertex, the size of the second largest ...

4
votes

1
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193
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Let $\mathcal{M}$ be a
locally finitely presentable model category, cofibrantly generated by
two sets $\mathcal{I}$ and $\mathcal{J}$ of cofibrations and trivial
cofibrations with presentable domain ...

3
votes

1
answer

111
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It is a famous result due to Riesz that every bounded linear functional $f$ on a Hilbert space $\mathcal{H}$ is of the form $f(x)=\langle x,z \rangle$ for a unique $z\in H$.
On p.188 of Introductory ...

2
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1
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130
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We know that a coherent sheaf on a scheme is determined by its restriction on certain open coverings (satisfying compatibility condition). Now I wonder how about a closed covering. To do so I started ...

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0
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70
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These days I have been reading about Keller's cube tyling conjecture, which asks if in any covering of $\mathbb{R}^n$ by translates of $[0,1]^n$ with disjoint interiors there are two cubes sharing one ...

3
votes

1
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93
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I am trying to understand more about geometric interpretation of vertex algebras following "Vertex Algebras and Algebraic Curves" by Ben-Zvi and Frenkel, but I am in trouble with the ...

3
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0
answers

53
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I want to find a general reference on topological and measurable dynamics of continuous piecewise linear interval maps. I am particularly interested in cases with only three pieces. I know there are ...

5
votes

1
answer

192
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As the title says. Which finite projective planes admit a symmetric incidence matrix?
I am not an expert in the field at all, but I consulted with one. He claimed that $PG(2, \mathbb F_q)$ can always ...

4
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1
answer

165
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Let $K$ be a number field i.e. a finite extension of $\mathbb{Q}$, $\overline{K}$ a fixed separable closure of $K$, and $G_K:=\mathrm{Gal}(\overline{K}/K)$ the absolute Galois group of $K$. Let $S$ be ...

9
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1
answer

405
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Suppose we are given embeddings $f_1,f_2:[0,1]\to\mathbb R^3$.
Does there exist a homeomorphism $g:\mathbb R^3\to\mathbb R^3$ such that $g\circ f_1=f_2$?
This question seems to be classical eighty ...

1
vote

1
answer

185
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Let
$\Omega$ be a metric space,
$C_b(\Omega)$ the space of all real-valued bounded continuous functions on $\Omega$, and
$\mathcal{M}(\Omega)$ the space of all finite signed Borel measures on $\Omega$...

4
votes

2
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169
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I'm reading a proof of below theorem from this paper.
Theorem A.3. Let $\Omega$ be a locally compact normal Hausdorff space. Let $\left\{\mu_n\right\} \cup\{\mu\} \subset \mathcal{M}(\Omega)$ and ...

2
votes

1
answer

56
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According to Wikipedia,
However, many results from classical harmonic analysis and computational geometry extend to the setting of metric spaces with doubling measures.
My question is: what are some ...

6
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3
answers

832
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A function $f:\mathbb{R}\rightarrow \mathbb{R}$ has a removable discontinuity at a given real $x$ in case the left and right limits are equal but not to the function value, i.e. $f(x+)=f(x-)$ but $f(x)...

25
votes

1
answer

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Update. It's now on the arXiv.
Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof (link removed, see arXiv). It is quite ...

7
votes

0
answers

102
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Endow $\mathbb{C}^{d \times d}$ with the norm induced by the Euclidean norm on $\mathbb{C}^d$. It is well-known (to those who know it well, I guess) that the spectrum $\sigma(A)$ of a matrix $A \in \...

1
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1
answer

228
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I am studying diophantine equations and I need the theory of Bakers, Can you advise me about good books, or lectures on Baker theory?

2
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1
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120
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Given a topological space $(X,\tau)$, recall that a cover $\mathcal{U}$ of $X$ is locally finite if for every point $x\in \mathcal{U}$ has a neighborhood $U$ that intersects finitely many elements of $...

2
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0
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81
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Let $(K,\mathcal{O},k)$ be a large enough $p$-modular system, where $\mathcal{O}$ is a complete discrete valuation ring of characteristic zero with unique maximal ideal $J(\mathcal{O})$, algebraically ...

8
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1
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109
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Let $C$ be a category. There is a full subcategory $\text{IdemMnd}(C) \hookrightarrow \text{Mnd}(C)$ of the category of monads on $C$ spanned by the idempotent monads. Given a monad $T$ on $C$, ...

7
votes

2
answers

444
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Suppose $a,b$ are two positive-definite linear operators on (say) $\mathbb R^n$. For $p\in(0,1)$, do we then have $(a+b)^p\leq a^p+b^p$ (with respect to the Loewner order)?

0
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0
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42
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I am interested in how the singular value decomposition relates to congruence transformations.
Suppose $X$ is positive definite of full rank $n$, and $X_k$ is the best rank $k$ approximation of $X$ in ...

3
votes

1
answer

138
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Some years ago, I found a paper with all the formulas for the balls into bins problem when the "areas" (i.e., probabilities to capture a ball) of the bins are all different. However, the ...

0
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0
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77
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This is a reference request for the following modern formulation of one of the central results of mathematical physics—Newton’s deduction of the inverse square law from Kepler’s description of the ...

12
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1
answer

344
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I would like to read Pincus' article Adding dependent choice, where he proves, among other things, the consistency of the theory $\mathsf{ZF+DC+O+\neg AC}$, where $\mathsf{DC}$ stands for Dependent ...

2
votes

1
answer

137
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Let $\mu$ be the Haar measure defined on the space of unimodular lattices, identified with $\text{SL}(d,\mathbb R)/\text{SL}(d,\mathbb Z)$.
The classical Siegel's formula in geometry of numbers states ...

0
votes

1
answer

68
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The Ito-Levy decomposition is well-known as a characterization of Levy processes. What does it give for the specific case of $\alpha$-stable Levy processes?

4
votes

1
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119
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Throughout I'm only interested in the standard semantics for second-order logic, and all structures/languages are relational for simplicity.
If defined naively, second-order logic without equality is ...

2
votes

1
answer

65
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I am working on a problem that involves an iterative application of a function I think might be a trapdoor function.
Formally, I have a function $f:X \to X$ that can be described as
$$
[x_{1,N+1}, ...,...

1
vote

0
answers

66
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In Tables of cellular automata, p.542, Wolfram defines the density $\delta$ of a rule to be the asymptotic density of nonzero sites when the initial configuration has density $1/2$. Wolfram quotes ...

3
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1
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72
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Many information theoretic quantities such as entropy and relative entropy appear in rate functions in large deviation theory (LDT). Is there any result in LDT that relates mutual information and rate ...

1
vote

1
answer

106
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Given two random variables $X,Y$ which are both $\mathbb{N}$-valued and have the same expected value (which is some fixed positive constant), and denote their probability mass functions by ${\bf p} = (...

1
vote

1
answer

92
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Does the category of measurable spaces have a strong subobject classifier (specifically $2 = (\{0,1\}, \{\varnothing, \{0,1\}\})$?
I would think the situation could be analogous to $\mathsf{Top}$, ...

2
votes

1
answer

89
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In the theorem below $P_D$ means the heat kernel in the open $D \subset \mathbb{R}^m$ and $P_m$ is the heat kernel in whole $\mathbb{R}^m.$
I know absolutely nothing about what Brownian bridges are, ...

3
votes

1
answer

116
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Suppose $p$ is a prime, that $F$ is a finite extension of the field $\mathbb{Q}_p$, $D$ is the division quaternion algebra over $F$ and $\mathcal{O}_D$ is the valuation ring of $D$. What is the ...

2
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0
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113
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I've found a formula for a scalar product in barycentric coordinates which I think is pretty cool. I hope that it's new. Is it?
Suppose that you have points $x_1,\dots,x_n$ sitting in general position ...

3
votes

2
answers

270
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I am interested in the following congruence
$$\binom{ap^n}{bp^n}\equiv \binom{a}{b}\pmod{p^n}$$
I am aware that by some reference in a book the above it should actually hold modulo $p^{3n}$; the ...

7
votes

1
answer

181
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Let $K$ be a global field (ie either a number field or the function field of a curve over a finite field). Let $A,B$ be abelian varieties over $K$ and let $\phi:A\to B$ be an isogeny. Associated with $...

9
votes

2
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373
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$\def\CC{\mathbb{C}}\def\RR{\mathbb{R}}$I am writing up notes on totally positivity in flag varieties. I often have the following situation: I have a complex variety $X$ defined over $\RR$ and a real ...

2
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0
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117
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Let $(X,O_{X})$ be a ringed space and $\mathcal{F^{\bullet}}$ be a bounded below complex of $O_{X}$-modules on $(X,O_{X})$. On [Stacks Project 20.25.1][1] it is shown that there is a weakly convergent ...

6
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0
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52
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By a Tarski space I understand a mathematical structure $(X,B,E)$ consisting of a set $X$, a ternary betweenness relation $B\subseteq X^3$ and a 4-ary equidistance relation $E\subseteq X^2\times X^2$ ...

9
votes

0
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179
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Is there an argument in the litterature that show that every locally presentable $\infty$-category is equivalent to the localization of proper combinatorial Quillen model category ?
Of course if one ...

9
votes

1
answer

139
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Given a strictly positive real number $x$ we set $e(x)=\log(1+x)$ if $x$ is an integer and
$$e(x)=\log(1+x)+\frac{1+\lbrace x\rbrace}{1+x}\left(e(1/\lbrace x\rbrace)-\log(1+\lbrace x\rbrace)\right)$$
...

10
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3
answers

931
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Certain categories of mathematical structures have had synthetic axiom systems developed for them. One particularly well known such category is the category of sets and functions $\mathit{Set}$, which ...