Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
15,748 questions
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Ramanujan's work on the central factorial numbers
Background
The central factorial numbers are described on OEIS sequence A008955. Among the references, "Ramanujan's notebooks, part 1" (edited by Bruce Berndt) is listed. Upon checking this ...
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For an infinite set S, I believe that all automorphisms of Sym(S) are inner. I would like a reference for this
For an infinite set S, I believe that all automorphisms of Sym(S) are inner. I would like a reference for this.
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Literature on the synthesis between Algebraic Geometry,Topology and Ergodic theory [closed]
Can you provide literature (books,papers etc) that combine ideas from these three fields together? AG,AT and ET.
Thanks!
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Possible asymptotic behavior of recurrence function
I was wondering and tried to find what are the results known related to recurrence function of a minimal subshift $\Omega \subseteq A^{\mathbb{Z}}$, where $A$ is finite non empty subset.
If I am not ...
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Is this strengthening of the Maynard-Tao theorem on primes in admissible tuples known?
The groundbreaking work of Maynard and Tao showed the following fundamental result:
For any integer $m$, there exists a number $k(m)$ such that for any admissible set $H$ of $k$ integers (with $k$ at ...
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Testing equal count between pairs of sets
For each fixed positive integer $N\in\mathbb{N}$, let's define two sets
\begin{align}
A_N:=&\{(a,b)\in\mathbb{N}^2: N=a(2b-1)+(2a-1)(b-1)\}, \\
B_N:=&\{(c,d)\in\mathbb{N}^2: N=c(2d-1)+(d-1)(d-...
- 43.8k
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Reference-request in deformation theory
Let $X$ be a smooth projective variety, and $Z\subset X$ a smooth closed subvariety of $X$. The first order deformations of $Z$ in $X$ are parameterized by $H^0(Z, N_{Z/X})$, while the first order ...
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Name for "continued fraction" matrices and the group they generate
Let $R$ be a ring. Is there a standard name for matrices of the form
$$
\begin{pmatrix}a & 1\\ 1 & 0\end{pmatrix}\in \mathbb{M}_2(R)?
$$
When $R=\mathbb{Z}$, these matrices arise naturally in ...
- 19.3k
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Literature for checking a function is c-concave
I would like to know if there is some update about checking a given function is $c$-concave, especially when $c$ is not (strongly) convex. Here we say $f$ is $c$-concave if $f$ is the $c$-transform of ...
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Reference request: Connectivity of the space of convex $n$-gons
I'd like a quick reference for the following fact: Let $(p_1, p_2, \ldots, p_n)$ and $(q_1, q_2, \ldots, q_n)$ be two convex $n$-gons in $\mathbb{R}^2$, both oriented clockwise. Then there are ...
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Existence for second order elliptic PDE with Robin boundary conditions reference
The paper I am reading is considering the following PDE:
$$
- \nabla \cdot \nabla \rho + (1 - 2 \bar{\rho}) \nabla \rho \cdot u =0
$$
on bounded $\Omega \subset \mathbb{R}^n$ ($n=1,2,3$) with $C^2$ ...
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Square-free integers: direct approaches vs. sums of $\mu(n)$
Let $Q(x)$ denote the number of square-free positive integers $\leq x$. Let $R(x) = Q(x) - \frac{x}{\zeta(2)}$.
There is a long literature (starting with Axer (1911) and continuing, starting ca. 1980, ...
- 21.9k
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Variant of van der Corput's kth-derivative estimate
I ask this question as a non-expert in analytic number theory who needs to use a number theory result. Lemma 2.2 of this paper by Chan, Kumchev and Wierdl reads as follows:
Lemma 2: Let $k \ge 2$ be ...
- 13.1k
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Simplicial complexes arising from Young diagrams and their homotopy type as wedges of spheres
My coauthors and I are finishing a paper in combinatorial and topological algebra, in which we define a class of simplicial complexes arising from Young diagramin the following way.
Let $\lambda = (\...
- 1,357
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Alternative, descriptive terminology for "Kleisli category"
Every monad is induced canonically by two universal adjunctions, introduced respectively by Kleisli and by Eilenberg and Moore. Since neither paper introduced names for the corresponding categories, ...
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Reference Request: Second Order Tauberian Theorem
I am interested in whether there exist Tauberian theorems for deducing the second order asymptotics of a particular function.
Throughout this post I am using the notation from Kwaśnicki's answer to ...
- 101
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Deformation quantization in mixed characteristic
We have well-known the theory of deformation quantization in characteristic $0$ (following the most recent Toën et al. "Shifted Poisson Structures and Deformation Quantization"), which for ...
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References for this law?
Let $S$ be a symmetric simple random walk starting at $0$ and denote by $p_{n,k}$ the probability $S$ occupes $k\in\mathbf{Z}$ at time $n\in\mathbf{N}$. For any $n\in\mathbf{N}$ denote also $q_n=\left(...
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Upper bound for maximum of reciprocal of zeta
The following appears in this paper:
Lemma Let $H=T^{1/3}$. Then we have
$$\min_{T\le t\le T+H}\max_{1/2\le\sigma\le 2}\frac{1}{|\zeta(\sigma+it)|}<\exp(C(\log\log T)^2)$$
where $C$ is an absolute ...
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What is the Alexander isomorphism for simplicial complexes, explicitly?
Let $X$ be a triangulation of an $n$-sphere, and $T \subseteq X$ be a subcomplex. There is a polyhedral complex $\bar{X}$ homoeomorphic to the $n$-sphere whose cells $\bar{\sigma}$ are in bijection to ...
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SZC implies explicit formula for Mertens function
To my understanding there is currently no proof of SZC (Simple Zeros Conjecture) implies
$$M_0(x)=\lim_{T\to\infty}\sum_{\zeta(\rho)=0\text{ and }\vert\Im(\rho)\vert\leq T}\frac{x^\rho}{\rho\zeta'(\...
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Minimum # of black squares to guarantee uniqueness of loop visiting all white squares
I asked this question on mathstackexchange, where more details and attempts are given. Given an $n \times n$ grid of white cells, what is the minimum number of black cells you need to shade such that ...
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Great theorems with elementary statements: 2026-onward
My 2021 book
Landscape of 21st Century Mathematics, Selected Advances, 2001–2020
collects great theorems with elementary statements published in 2001-2020. I now finishing the second edition of this ...
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The relation between Temperley-Lieb algebra and representations of $U_q \mathfrak{sl}_2$
What is a good modern reference (or maybe this is known to someone here and lacks a good reference) which explains the relation between the Temperley-Lieb algebra and representations of $U_q(\mathfrak{...
- 3,454
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Reference request: the $\omega_2$'th canonical function does not exist
For functions $f, g: \omega_1 \to \mathrm{Ord}$, put $f <^* g$ if $\{\gamma < \omega_1: f(\gamma) < g(\gamma)\}$ contains a club, likewise define $=^*$ and $\leq^*$ (notice that, assuming ...
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