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 ...
- 27
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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 ...
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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,...
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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
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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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1
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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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Selberg's result on primes in short intervals
A result of Selberg (A. Selberg. On the normal density of primes in small intervals, and the difference between consecutive primes. Arch. Math. Naturvid., 47(6):87–105, 1943) says essentially
$$\int ...
- 1,656
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1
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Injectivity of derivations from the middle transvectant in the free Lie algebra on $\operatorname{Sym}^m$ for $\mathrm{SL}_2$
Let $G=\mathrm{SL}_2(\mathbb C)$, $V$ its standard representation, and $V_m=\operatorname{Sym}^m(V)$ with $m\equiv 2 \pmod 4$. It is classical that
$$
\Lambda^2 V_m \;\cong\; \bigoplus_{\substack{1\le ...
- 3,366
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K-flat complexes and unbounded derived tensor product over a non-commutative sheaf of rings
$\def\R{\mathscr{R}}
\def\O{\mathcal{O}}$Let $X$ be a topological space and let $\R$ be a sheaf of unital non-commutative rings over $X$.
When $\R$ is commutative, there is much literature on ...
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Reference for freeness of the ring generated by roots of unity
The following fact is well-known, and not hard to prove, but I do not know an explicit reference.
Let $R$ be the subring of complex numbers generated by all roots of unity. Then $R$ is free as an ...
- 782
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answer
363
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Coefficient comparison between a double sum and a single sum
For a formal Laurent series $F(q)$, denote its coefficient of $q^j$ by $[q^j](F)$.
QUESTION. For integers $r\geq1$, is this true?
$$[q^{2r}]\sum_{n\geq1}\frac{q^n}{1-q^{2n}}\sum_{k=1}^n\frac{q^k}{1+q^...
- 43.9k
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(Cohomological) Brauer group of $BG$ — reference request
Let $G$ be a smooth connected linear algebraic group over an algebraically closed field. Write $\operatorname{Br}'(BG)$ for the cohomological Brauer group of $BG$, i.e. the group of $\mathbb{G}_m$-...
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Measurability of $t \mapsto \int_A f(t, \omega)\mathbb{Q}_t(\mathrm{d}\omega)$ when $(t, \omega) \mapsto f(t, \omega)$ is not measurable in $t$
I have a Markov kernel $(t,A) \mapsto \mathbb{Q}_t(A)$ from a standard Borel space $(T, \mathcal{T})$ into another standard Borel space $(\Omega, \mathcal{F})$. Also, for $t \neq s$, $\mathbb{Q}_t \...
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Like circle packing but not exactly
I am looking for bibliography on the following problem.
Given $N\in\mathbb{N}$ find $N$ points $p_1,...,p_N\in\mathbb{R}^2$ which
(1) maximize $\min_{i,j} |p_i-p_j|$
(2) subject to the constraint $\...
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