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Questions tagged [reference-request]

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

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Sufficient condition for the absolute convergence of Fourier series of a function on the adele quotient $\mathbb A_k/k$

Let $G$ be a compact abelian group. The unitary characters of $G$ form an orthonormal basis of $L^2(G)$, so every square integrable function $f: G \rightarrow \mathbb C$ admits a Fourier expansion $$...
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0answers
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+300

Continuity of Intersection Pairing on Chow monoids

Let $X$ be a smooth irreducible complex projective variety. As we know, if $\alpha,\beta$ are two cycles intersecting properly in $X$, we can define, via Serre's Intersection Formula, their ...
3
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1answer
76 views

Partition Calculus and Ramsey theory question

These topics are outside of my area of research, so I am not quite sure where in the literature to find the answers. In what follows, if $X$ is partially ordered and $n$ is a natural number, let $[[...
5
votes
1answer
159 views

Sheaves over a sheaf

Everything I write I mean in the in the sense of Lurie's HTT. Suppose that $ \mathcal{C}$ be a site and let $ F \in Fun( \mathcal{C}^{op} , \mathcal{S})$. Is it always/ever true that $ Sh(\mathcal{C}...
5
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1answer
159 views

Discrete Wavelets

I am looking for research that has been done in Discrete wavelets. Let me be specific as Google doesn't give me what I want when I say "discrete wavelets". I don't want countable basis for $ L^2(\...
4
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1answer
297 views

Reference request for Kato's paper: A generalization of local class field theory by using K -groups

I would like to ask for the paper of Kato: A generalization of local class field theory by using K -groups I, J. Fac. Sci. Univ. Tokyo Sec. IA 26 No.2, 1979, 303–376. I could not find it. Could anyone ...
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2answers
558 views

Linking topological spheres

Is there a simple proof of the fact that: If $A\subset S^3$ is homeomorphic to $S^1$, then there is a circle $B$ embedded into $S^3\setminus A$ that such that the circles $A$ and $B$ are ...
14
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1answer
650 views

The state of the art in the rectification of homotopy-coherent structures

My question concerns rectification theorems for homotopy-coherent structures. As the meaning of this may be unclear, let me list a few examples of what I am thinking of: Cordier and Porter proved a ...
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1answer
98 views

If $p_n(a,b)$ is a rational number (or integer) for 3 consecutive values of $n$ then every $p_n(a,b)$ is

Let $a$ and $b$ be two real numbers and $p_n(x,y)$ the polynomial: $$p_n(x,y)=\sum_{i=0}^{n-1}x^{n-1-i}y^{i},$$ where $n$ is a positive integer. In a previous post I asked if $p_n(a,b)$ was a ...
5
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1answer
146 views

One particle irreducible Feynman diagrams

In quantum field theory Feynman has invented a diagrammatic method to encode various terms in the Taylor decomposition of integrals of the following form below which I will write in a baby version as ...
4
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4answers
190 views

Bijective operations on finite simple graphs

Let $\mathcal G_n$ be the set of (isomorphism classes of unlabelled) simple graphs on $n$ vertices. I am interested in specific bijective maps $\mathcal G_n\to\mathcal G_n$, defined for all $n$. An ...
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0answers
103 views

Quantum Hamiltonian reduction and Quantum Airy structure

I have been reading Kontsevich and Soibelman's "Airy structures and symplectic geometry of topological recursion" (https://arxiv.org/pdf/1701.09137.pdf) and having trouble understanding their Section ...
7
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1answer
114 views

equidistributed parameters on graphs

Let $\mathcal G_n$ be the set of (isomorphism classes of unlabelled) simple graphs on $n$ vertices. I wonder whether there are any 'interesting' combinatorial parameters $a,b: \mathcal G_n\to \mathbb ...
2
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1answer
90 views

Can we extract information from signature (rough path theory) to construct part of signal?

This question is related to rough path theory. Consider we have obtained signature obtained from a set discrete data points postulating linear from one data point to another. Such signature are used ...
24
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1answer
576 views

Littlewood’s three precepts of refereeing in mathematics: is it (1) new, (2) correct, (3) interesting?

I have a question regarding Littlewood’s three precepts of refereeing a mathematical paper, namely whether it is (1) new, (2) correct, and (3) interesting. I have found these mentioned in the ...
18
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1answer
767 views

Is there any publication of Bombieri about the standard conjectures on algebraic cycles?

In "Standard conjectures of algebraic cycles" Grothendieck says: "... These [Standard conjectures] are not really new, and they were worked out about three years ago independently by Bombieri and ...
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0answers
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+50

Rate of convergence for difference between conditional and marginal probability

Suppose $X\sim \text{Bin}(2n,p)$ and $X_1,X_2\sim\text{Bin}(n,p)$ are independent, with $X_1+X_2=X$. I'm interested in the rate of convergence for the absolute difference $$ \left\vert P(X>c|X_1\...
7
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3answers
933 views

Transforming a binary matrix into triangular form using permutation matrices

I am interested in the complexity of the following problem: Given an $m\times n$ binary matrix $M$, can we permute its rows/columns to obtain a triangular matrix? I am also interested in ...
1
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2answers
157 views

Reference request: Functions of bounded variation in one real variable

Is there a good reference for facts and theorems about BV real valued functions? I’m looking for something with much more than say Stein and Shakarchi 3, or Evans and Gariepy. Thanks!
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0answers
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smoothness of Hurwitz spaces with arbitrary ramification profiles

Fix integers $n\ge 3,d\ge 2$, and partitions $\lambda_1,\ldots,\lambda_n$ of $d$. Let $\mathcal{H}$ be the moduli space of degree $d$ covers $f:C\to\mathbb{P}^1$ that have ramification profiles $\...
2
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1answer
59 views

Quasilinear elliptic problem: Ellipticity-type conditions

Consider the following quasilinear elliptic equation $$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$ on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\...
2
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0answers
39 views

Holomorphic Poisson structures on $C P^{n-1}$ and homogeneous Poisson structures on $C^n$

Is it correct that any holomorphic Poisson structure on $C P^{n-1}$ can be lifted to a homogeneous Poisson structure on $C^n$? By homogeneous I mean a quadratic Poisson structure of the form $\{z_i,...
11
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3answers
504 views

is this a modular form of some kind?

I suspect that the function $$F(q) = \sum_{n \geq 0} (2n + 1) \, q^\binom{n+1}{2}$$ may be some kind of modular form. It looks like a weighted theta function, but is not exactly an harmonic theta ...
2
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1answer
96 views

Local Sobolev embedding on complete Riemannian manifold

Let $(M,g)$ be a complete Riemannian $m$-manifold, with bounded geometry and $m\geq2$. Suppose $Ric\geq(n-1)\kappa$. Let $B_p(r)$ be a geodesic open ball. Q Can we find a constant $C=C(\kappa,r,m)$(...
1
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1answer
52 views

Name of a function space

For a real function $f$ on $\mathbb{R}$, define $e_n(f)$ to be the infimum of the $L_1$ distance between $f$ and piecewise constant functions on the subdivision of $\mathbb{R}$ into intervals of ...
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0answers
42 views

The Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\sqrt{-3})$

I'm now on a research about the Iwasawa $\lambda$-invariants of the cyclotomic $\mathbb{Z}_p$-extensions of number fields. And it happens that the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\...
2
votes
1answer
219 views

Original sources for two theorems by Bass, Matlis and Papp

It is an interesting fact that a commutative ring $R$ is noetherian if and only if direct sums of injective $R$-modules are injective, and if and only if every injective $R$-module is a direct sum of ...
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0answers
19 views

Reference request: Numerical methods for Hamilton-Jacobi-Bellman equations with state constraints

I have two questions on numerical methods for solving Hamilton-Jacobi-Bellman (HJB) equations with state constraints. Consider an optimal control problem given by $$ v(x) = \max_{\{u(t)\}_t} \int_o^\...
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1answer
421 views

Literature about most basic existence proofs in graph theory [closed]

I'm writing a MIZAR article about foundations in graph theory e.g. constructing a supergraph from a given graph by adding a vertex to it. The main theorem of the article will be that any graph ...
2
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1answer
114 views

Fixed points of the automorphisms of sporadic groups

Sporadic groups have very few outer automorphisms (in fact, $|\mathrm{Out}(G)|\leqslant2$), so it is very natural to ask what are the fixed points subgroups. For a group of Lie type (and a suitable ...
5
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1answer
172 views

Functional equation for general number fields

When it comes to general number fields beyond $\mathbb{Q}$, the litterature is not so abundant in analytic number theory. For instance over $\mathbb{Q}$, for primitve Dirichlet characters modulo $q$, ...
3
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1answer
232 views

Is it possible to define a linear $A_\infty$-category as a special kind of an $\infty$-category?

A functor $N\colon\mathrm{Cat}_{A_\infty}\longrightarrow\mathrm{Cat}_\infty$ is constructed in a paper [1] by Faonte. This gives a way to get an $\infty$-category by starting with an $A_\infty$-...
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1answer
236 views

Are there nice isomorphisms $\operatorname{S}^2(k^n)\cong\Lambda^2(k^{n+1})$?

This might be forced to migrate to math.SE but let me still risk it. The spaces $\operatorname{S}^2(k^n)$ and $\Lambda^2(k^{n+1})$ from the title have equal dimensions. Is there a natural isomorphism ...
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0answers
68 views

Power of an integer as a sum of $\binom{n}{n-2}$ integers [on hold]

Consider the following equation $$ y^n=\sum_{k=1}^{\frac{n(n-1)}{2}} x_k, $$ where $x,y,n,x_k\neq 0$ are integers. Although I found a lot of material about how to express an integer as a sum of ...
6
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1answer
446 views

Famous but unavailable paper of Jan Boman

The following paper is well known, but hard to find: J. Boman, $L^p$-estimates for very strongly elliptic systems, Report 29, Department of Mathematics, University of Stockholm, 1982. In this paper ...
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4answers
4k views

Could the Riemann zeta function be a solution for a known differential equation?

Riemann zeta function is a function of complex variable $s$ that analytically continous the sum of Dirichlet series .defined as :$$\zeta(s)=\sum_{n=1}^{\infty}\displaystyle \frac{1}{n^s} $$ for when ...
3
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1answer
547 views

A new generalisation of dimension? part 2

I worked this theory : A new generalization of the dimension? I have a theorem about dimensions which is more general and simple than for matroids. Definition 1: A structure $S$, is a pair $(X, \...
7
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2answers
668 views

Does anyone know what is the right reference for the following simple lemma from harmonic analysis?

The lemma says that given $\lambda\geq 1$, $p\geq 1$, $a_j\geq 0$, for a collection of balls $\{B_j\}_{j\in\mathbb{N}}$ in $\mathbb{R}^n$, it holds $$\bigg\|\sum_j a_j\chi_{\lambda B_j}\bigg\|_p\leq C(...
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6answers
2k views

Geometric flavored textbook on algebra

I am interested in topology, while I am not so comfortable with some algebraic flavored textbook on algebra. Actually, it was not until I learned some topology that I began to understand some ...
3
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0answers
41 views

Proof that superstable theories with no Vaughtian pairs have no imaginary Vaughtian pairs

In 'Elementary pairs of models' by Bouscaren, she mentions with a remark at the end that if $T$ is a superstable theory then $T$ has a Vaughtian pair if and only if $T^\text{eq}$ has a Vaughtian pair, ...
0
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1answer
82 views

Analytic approach to geodesic connectedness in Semi-Riemannian manifolds

Can you point out a reference (or references) that deal with analytical methods (rather than methods from differential geometry) for the study of geodesic connectedness on Semi-Riemannian manifolds?
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0answers
26 views

Quasilinear elliptic problem on fractal domain

Consider the following quasilinear elliptic equation $$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$ on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\...
34
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2answers
2k views

Mathematical research in North Korea — reference request

Question: Where can one find information on which areas of mathematics are represented at which of the more than 20 universities in the Democratic People's Republic of Korea (DPRK), and on which ...
6
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0answers
113 views

Is there a version of Weyl's law for graph Laplacians?

Is there a version of Weyl's law or a local Weyl's law for eigenvectors of the graph Laplacian? For some context, a colleague in statistics has encountered eigenvectors of the Laplacian for certain ...
2
votes
0answers
28 views

Flat or linkless embeddings of graph with fixed projection

The problem of finding whether a given planar diagram of a graph, with over- and under-crossings, is a linkless embedding or not has unknown complexity (Kawarabayashi et al., 2010). My first question ...
5
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0answers
122 views

Beilinson and Deligne's Motivic Polylogarithm and Zagier Conjecture

Where can I find the preprint Motivic Polylogarithm and Zagier Conjecture by Beilinson and Deligne? I see it referenced in a lot of papers but no one seems to host a copy.
16
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2answers
818 views

A multicategory is a … with one object?

We all know that A monoidal category is a bicategory with one object. How do we fill in the blank in the following sentence? A multicategory is a ... with one object. The answer is fairly ...
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1answer
121 views

The quotients of double cosets $P_\theta \backslash P_\theta w P_\Omega$ are algebraic varieties over $k$

Let $k$ be a $p$-adic field, $G$ a connected reductive group over $k$ with minimal parabolic $P_0$ containing a maximal split torus $A_0$. Let $W = N_G(A_0)(k)/Z_G(A_0)(k)$ be the Weyl group, and $S \...
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3answers
503 views

Reference request for wild 3-manifolds

I’m looking for a text on 3-manifolds that focuses on wild/pathological objects, similar to Bing’s work in the field. I know basic algebraic topology (homotopy, homology, cohomology) and have read ...
2
votes
2answers
792 views

Reductive Lie algebra of a Lie group

In the answer of my question: On the full reducibility of representations of reductive Lie algebras James E. Humphreys replied to me saying that:"the notion of "reductive" for a Lie algebra in ...