Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
15,771 questions
13
votes
2
answers
412
views
Reference request: determinacy and Lebesgue-measurability locally
I've heard it said many times times that $\boldsymbol{\Pi}^{1}_{n}$-determinacy implies $\boldsymbol{\Sigma}^{1}_{n+1}$-Lebesgue measurability (hence for instance $n$ many Woodin cardinals with a ...
2
votes
0
answers
100
views
Optimal constant in $L^1-L^2$ inequality on Gauss space
For a differentiable real-valued function on $\mathbb{R}^n$, denoting $\partial_i f$ for the $i$th partial derivative, we can define the functional
$$
T_n(f) = \sum_{i=1}^n \frac{1}{1 + \log(\|\...
- 582
0
votes
0
answers
20
views
Reference request: Stability of strong diameter two property under infinite $\ell_1$-sums
Does anyone know a reference for the following result:
If $\{X_i\}_{i \in I}$ is a familiy of Banach spaces with the strong diameter two property, then its $\ell_1$-sum has this property too.
I'm ...
- 393
3
votes
0
answers
86
views
(Weak) Jordan-Chevalley decompositions over non-perfect fields
This is a reference/literature request.
Given a field $K$ and an endomorphism $x \colon V \to V$ of a finite-dimensional $K$-vector space it is well-known that the Jordan-Chevalley decomposition of ...
- 31
-1
votes
0
answers
79
views
Local Frobenius algebras, reference
I found this statement on wikipedia:
Commutative, local Frobenius algebras are precisely the zero-dimensional local Gorenstein rings containing their residue field and finite-dimensional over it.
Can ...
- 7
8
votes
1
answer
720
views
The fourth moment of the Riemann zeta function without absolute values
Are there any results known about the asymptotics/bounds for
$$\int_0^T\zeta(\tfrac{1}{2}+it)^4\;dt,$$
where we don't have the absolute value on the inside?
One could use the triangle inequality to ...
- 191
3
votes
0
answers
81
views
Reference request: Formula of Seifert invariant of Dehn surgery along torus knots
Is there a literature that contains an explicit formula of Seifert invariants
of 3-manifold $S^3_{T_{p,q}}(\frac{s}{r})$, the $\frac{s}{r}$-Dehn surgery on the $(p,q)$-torus knot $T_{p,q}$ ?
As for ...
- 918
1
vote
1
answer
232
views
Is total homology endo-functor, on bounded derived category of finitely generated modules over commutative Noetherian ring, a triangulated functor?
Consider the bounded derived category $D^b(\operatorname{mod } R)$ of finitely generated modules over a commutative Noetherian ring $R$ and the homology functor $H_*: D^b(\operatorname{mod } R) \to D^...
- 573
1
vote
0
answers
45
views
Shimura reciprocity for Drinfeld modular varieties?
let's suppose we have a function field $F$ and some Drinfeld modular variety of rank $r$ over $F$, with some level structure $Y^{(r)}(N)$. Then the field of constants of $Y^{(r)}(N)$ is some class ...
- 2,251
-6
votes
0
answers
141
views
Question on Baby Rudin's Th. 2.47 (3rd. ed.) [closed]
The theorem in question has to do with the classification of the connected subsets of $(\mathbb{R}, d_{\mathrm{eucl}})$. It reads as follows:
Th. 2.47. A subset $E$ of the real line is connected iff ...
- 9,123
4
votes
0
answers
108
views
Is there a real analytic tubular neighbourhood theorem?
The tubular neighbourhood theorem, stating that an embedded submanifold has a neighbourhood that is a diffeomorphic image of an open subset of the normal bundle, is a staple result about smooth ...
- 9,076
1
vote
0
answers
34
views
Justifying the Robbins-Monro procedure using Dvoretzky's theorem on stochastic approximation
A colleague and I are trying to understand some results in stochastic approximation theory with a view to gaining quantitative information about rates of convergence of certain processes. We have done ...
- 1,169
0
votes
0
answers
105
views
Spiral visualizations of Riemann Zeta function sampled at arithmetic progressions: has this been studied? [closed]
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 ...
- 55
3
votes
3
answers
686
views
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 ...
- 39
1
vote
0
answers
210
views
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,...
- 1,739