Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
15,759 questions
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Spiral visualizations of Riemann Zeta function sampled at arithmetic progressions: has this been studied?
While experimenting with visualizations of the Riemann zeta function on the critical line, I constructed the following object, which I have not seen discussed in the literature, and I would like to ...
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Compact connected Riemannian manifolds are Ahlfors regular metric space
Let $(M,g)$ be a compact connected $n$-dimensional Riemannian manifold; let $(X,d)$ denote its associated metric (length) space. A comment on the original formulation of this post mentioned that $(X,...
3
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1
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Injectivity of derivations from the middle transvectant in the free Lie algebra on $\operatorname{Sym}^m$ for $\mathrm{SL}_2$
Let $G=\mathrm{SL}_2(\mathbb C)$, $V$ its standard representation, and $V_m=\operatorname{Sym}^m(V)$ with $m\equiv 2 \pmod 4$. It is classical that
$$
\Lambda^2 V_m \;\cong\; \bigoplus_{\substack{1\le ...
- 14k
2
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2
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What literature can I read about the Janibekov effect and the intermediate axis theorem?
I have been studying mathematics for 2 years, and I have already read Terence Tao's publication. Please suggest books on related topics, such as Euler's equations, mathematical modeling, mathematical ...
- 1,095
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Recursive pointfree approach to algebraic topology
$\newcommand\seq[1]{\langle#1\rangle}$A large number of important topological results require simplicial-algebraic machinery (or comparable) to prove. This machinery is ingenious, impressively so even,...
- 14k
2
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49
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Projection onto translation invariant subspaces
I'm currently looking at a subspace of $A \subset \ell^p(\mathbb{Z}^n)$ which is generated by some finitely supported elements and their translations. My question is an old one (but the answer is ...
- 4,726
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Are two symplectic fibration(resp. Hamiltonian fibration) are smoothly fibration isomorphic if it holds continuously?
Let $P, P'$ be symplectic(resp. Hamiltonian) fibrations over a base $B$.
If two $P, P'$ are continuously symplectic fibration(resp. Hamiltonian fibration) isomorphic, then are they also smoothly ...
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Covering lattice points with planes and lines
The following question was asked on a Chinese contest:
Prove that there exists a real constant $c>0$ such that if all lattice points inside and on the boundary of a convex polyhedron in $ \mathbb{...
- 3,143
26
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2
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Does summing divergent series using cutoff functions give consistent results?
One way to try to give a value $S$ to a divergent series $\sum_{n=1}^\infty a_n$ is with a smooth cutoff function:
$$
S = \lim_{N\to\infty}\sum_{n=1}^\infty a_n \eta\left(\frac{n}{N}\right)
$$
where $\...
- 141
1
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1
answer
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Restrictions of metrics
A metric $d:M^2\rightarrow \mathbb{R}$ is any mapping that satisfies the well-known textbook definition of metric space $(M, d)$. In certain areas (optimal transport, topometric spaces, and quantum ...
- 1,739
3
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Reference for result on $p$-divisible groups
I'm currently working through Tate's paper on $p$-divisible groups and have come to an impasse in his discussion of tangent spaces of $p$-divisible groups. I'd like to show that for an abelian variety ...
- 438
2
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1
answer
364
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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(...
- 71
4
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1
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Basic properties of unitary Turaev-Viro skein spaces
The following kinds of things seem to be well-known, but I don't know of explicit references.
Consider Turaev-Viro TQFT based on a unitary spherical fusion category $\mathcal{C}$. To any surface $\...
- 173
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13
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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 ...
- 8,625
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1
answer
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Minkowski sum of finite ellipses
Let $(E_n)_n$ be any finite collection of centred ellipses in $\mathbb{R}^2$. Suppose that $E_n$ are pairwise non-homothetic (i.e. there is no positive constant $c>0$ such that $E_n = c E_m$). Now ...
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