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

**-2**

votes

**0**answers

93 views

### Are there “adelic” L-functions?

Following Tom163's answer to this question, I would like to know whether L-functions defined through adelic representations (as defined in https://projecteuclid.org/euclid.em/1317758108) have been ...

**2**

votes

**2**answers

124 views

### $\mathcal S'(\mathbb R^d)$ is separable

I Think the statement is true, but I struggle to find a reference for the fact that the space of tempered distributions equipped with the weak-* topology is separable.
Thank you for your help!

**-2**

votes

**1**answer

51 views

### How does deletion-contraction affect chromatic number? Can it increase chromatic number? [on hold]

Question: In graph theory, contracting an edge or deleting an edge are basic operations in many topics such as graph minors or Wagner's theorem on planar graphs. And I'm interested in how these ...

**0**

votes

**0**answers

29 views

### Reference request for some “irregularities of distribution” papers

I would like to ask if anyone has access to any of the following papers:
1. J. G. van der Corput, Proc. Kon. Ned. Alcad. v. Wetensch., Amsterdam, 38, 813-821
(1935).
2. J. G. van der Corput, ibid. 38, ...

**2**

votes

**2**answers

125 views

### Examples of toric threefolds

I am looking for examples of smooth projective toric threefolds $\mathbb P_\Delta$ such that the rational polytope $\Delta$ has only pentagonal faces and hexagonal faces.
I quickly searched for ...

**4**

votes

**1**answer

129 views

### Higher-dimensional category theory on objects

I would like to know if there exists a satisfying generalization of higher-dimensional category theory on objects, that doesn't forget the inner structure of objects. Usually, what people do is to ...

**2**

votes

**0**answers

95 views

### Correspondence between real forms and real structures on complex Lie groups

I asked this in MSE, but without success, so I hope, it will be suitable here.
E.B.Vinberg and A.L.Onishchik in their book give the following two definitions.
For a complex Lie group $G$ its real ...

**0**

votes

**0**answers

27 views

### interpolation between Bochner spaces

Is there a reference for the interpolation result stating the existence of an embedding
\begin{equation}
L^2(I;W^{2,p}(\Omega)) \cap H^1(I;L^p(\Omega)) \hookrightarrow ...

**6**

votes

**2**answers

173 views

### What methods do we have to understand the spectrum of matrices with restricted entries?

Consider questions of the form (or the "most probable value of" version of these questions rather than the "largest possible"),
What is the largest possible spectral radius of a $n \times n$ matrix ...

**4**

votes

**0**answers

75 views

### On various “extension closures” and “orthogonals” in triangulated categories

A vague form of my question is the following one: for a class of objects $D$ of a triangulated category $C$ we consider the class $E$ of objects that satisfy $Mor_{C}(d,e)=\{0\}\ \forall d\in D$; ...

**2**

votes

**0**answers

42 views

### Multiplication operators are sectorial [migrated]

Consider the multiplication operator $M_a$ on $L^p(M)$, where $M$ is a Riemannian manifold, and $a$ is a non-negative function. An operator $A$ is said to be sectorial if there exists $\theta \in (0, ...

**3**

votes

**1**answer

128 views

### Preprint by Wall on Sjogren's theorem

In their account http://dx.doi.org/10.1016/0022-4049(87)90048-X of Sjogren's theorem, Cliff and Hartley refer to two articles:
[9] B. Hartley, A note on a lemma of Sjogren relating to. dimension ...

**3**

votes

**0**answers

84 views

### n-homology of a Harish-Chandra module

Let $G$ be a connected real reductive Lie group and let $K$ be its maximal compact subgroup.
Let $P=MAN$ a parabolic subgroup. Let $K_M^0=M^0\cap K$ be connected component of the maximal compact ...

**2**

votes

**0**answers

60 views

### Resolvent estimate of hyperbolic Laplacian [on hold]

Consider the Laplacian $-\Delta$ on the hyperbolic space $\mathbb{H}^n$. For $\lambda \in \mathbb{C} \setminus [0, \infty)$, do we have resolvent estimates of the form
$$\Vert (-\Delta - \lambda ...

**3**

votes

**3**answers

176 views

### Enumerating cosets of the modular group

Suppose we chose the generators $f(z) = z+1, g(z) = z-1, h(z) = -1/z$ for the modular group $\Gamma$ (i.e. the group of fractional linear tranformations $z \mapsto (az +b)/(cz+d)$ with $a,b,c,d \in ...

**2**

votes

**0**answers

154 views

### References for 'Theory of $p$-adic Galois Representations by Fontaine & Ouyang'

Presently I am reading the 'Theory of $p$-adic Galois Representations by Fontaine & Ouyang'. I am finding it difficult for eg. the initial sections on $l$-adic geometric representation of finite ...

**3**

votes

**1**answer

155 views

### Model structure on non-negative differential graded algebras with homological grading

I was wondering if there exists a model structure on the category of non-negative differential graded algebras with homological grading. To be more precise: Let $Ch_{k}$ the model category of ...

**3**

votes

**0**answers

60 views

### Localized at $p$ integral representations of finite elementary $p$-groups

Let $C_p$ be a cyclic group of prime order $p$.
Let $F=C_p^n=C_p\times\dots\times C_p$ ($n$ times).
I would like to to classify finite dimensional representations of $F$ over ${\mathbb{Z}}$.
However, ...

**0**

votes

**1**answer

58 views

### Reference for measures of commutativity needed

I'm looking for an appropriate measure to quantify the extent to which two matrices commute. In other words, if A and B are two n×n Hermitian matrices, and [A,B]=C.
I'd like a function μ:Cn×n→[0,∞) ...

**7**

votes

**0**answers

110 views

### Complete list of exceptions and efficient algorithm for Waring's problem

2 weeks ago, Samir Siksek http://arxiv.org/abs/1505.00647 proved more than 150-years-old conjecture that every positive integer other than 15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, ...

**0**

votes

**0**answers

44 views

### Global existence solutions NLS

Let's consider the following NLS in $\mathbb{R}^3$
$$i\partial_t\psi=-\Delta\psi+\vert\psi\vert^2\psi$$
How to prove that $H^2$-solutions are globally in time? Can someone suggest references to me?

**3**

votes

**0**answers

55 views

### Integrability of Continuous Tangent Subbundles

Are there any field of mathematics, except dynamical systems, where one needs to integrate continuous sub-bundles of the tangent space?
More specifically given a smooth manifold of $M$ and a ...

**4**

votes

**2**answers

171 views

### hyperbolic structure on Figure–8 knot complement

I was trying to understand the proof of the fact that there is a hyperbolic structure on Figure–8 knot complement initially from Thurston's notes and then from some online notes; but unfortunately I ...

**0**

votes

**0**answers

51 views

### Sum of weighted permutations over natural numbers [on hold]

If we consider the sum $\sum\limits_{i=1}^n i\sigma(i)$ where $\sigma$ is a permutation of the first $n$ natural numbers, then this sum has a few interesting properties for various values of $n$. My ...

**5**

votes

**2**answers

199 views

### Where is the exponential map a diffeomorphism?

Let $M$ be a closed compact Riemannian manifold.
The exponential map $\mathrm{exp}:TM\to M\times M$ takes $(p,v)$ to $(p,\gamma_v(1))$, where $\gamma_v$ is the geodesic flow at $p$ in the direction ...

**1**

vote

**0**answers

74 views

### On moduli space of torsion free semi-stable sheaves on nodal curves

Let $X$ be a projective irreducible nodal curve of genus at least $2$. Denote by $U(r,d)$ the moduli space of semi-stable torsion free sheaves on $X$ of rank $r$ and degree $d$. There are several ...

**4**

votes

**1**answer

131 views

### Upper bound of the waiting time of a sum process

Let $n \in \mathbb{N}$, $x_1, \ldots, x_n \in (0,1)$ fix but arbitrary, s.t. $\sum_{i=1}^n x_i = 1$. Let $X_i \sim \operatorname{Unif}(\{x_1, \ldots, x_n\})$ i.i.d., and $T_n = \min\{t \in \mathbb{N} ...

**3**

votes

**1**answer

131 views

### Fixed point property for intersection of spaces which are homeomorphic to a disk

The following question is question 9.8 from Miller's paper ``Some interesting problems
'':
Question Suppose $D_n$ a subset of the plane is homeomorphic to a disk and for every
$n\in \omega, ...

**7**

votes

**0**answers

242 views

### Godel's second incompleteness theorem for non-r.e. theories

R. Jeroslow in this paper proves that a non-recursively enumerable theory whose set of theorems is $\Delta_2$-definable may prove consistency of itself
but it can not prove 2-consistency of itself.
...

**3**

votes

**0**answers

62 views

### Idempotent relations on the unit square with closed graphs

A colleague and I are interested in idempotent relations from $I=[0,1]$ to $I$ - relations such that $R\circ R(x)=R(x)$ for all $x\in I$. Specifically, the graphs of the relations we care about must ...

**7**

votes

**0**answers

166 views

### May's infinite loop machine for Friedlander's result for Adams conjecture

Eric M. Friedlander in the paper The infinite loop Adams conjecture via Classification Theorem for $\Gamma$-spaces proved the infinite loop Adams conjecture using techniques involved $\Gamma$-space.
...

**5**

votes

**1**answer

373 views

### Vectorisation of a category

I have no experience with category theory at all, but I recently stumbled upon the following construction. Since it is extremely elementary and seems rather natural, it should be known, but I have not ...

**0**

votes

**0**answers

40 views

### Looking for Information on Local Degree of Maps on Homology Manifolds

By a homology $n$-manifold, we mean a topological space $X$ such that for all $x \in X$:
1: if $k \neq n$ then $H_k(X, X-x)=0$
2: $H_n(X,X-x) \cong \mathbb{Z}$.
Given homology $n$-manifolds $X$ and ...

**6**

votes

**1**answer

127 views

### On the independence of lower and upper asymptotic and Banach densities

Given a set $X \subseteq \mathbf N^+$, denote by $\mathsf{d}_\ast(X)$ and $\mathsf{d}^\ast(X)$, respectively, the lower and upper asymptotic (or natural) density of $X$, viz. $$\mathsf{d}_\ast(X) := ...

**1**

vote

**0**answers

138 views

### Reference request: Cohomology of Elliptic Curves

Is it true that the group
$$H^1(Gal(K^{ab}/K)/\mu_{\nu}(Gal(K_{\nu}^{ab}/K_{\nu})),E_{p^n})$$
is always p-divisible? Or are there any conditions which, when satisfied, guarantee its p-divisibility?
...

**9**

votes

**1**answer

391 views

### On a result attributed to W. Ljunggren and T. Nagell

I've read in a number of places that, building on previous work of T. Nagell, W. Ljunggren proved in 1 that the Diophantine equation
$$\frac{x^{n}-1}{x-1} = y^{2}$$
doesn't admit solutions in ...

**9**

votes

**2**answers

645 views

### How to learn QFT from mathematical perspective?

I want to learn QFT, because I have heard of its applications in mathematics, I am not interested in scattering cross sections and such. Where can I start to learn? Only books I found are either way ...

**9**

votes

**1**answer

238 views

### Sard's Theorem For Banach Spaces

Given a smooth map from $\phi: B \rightarrow M$ where $B$ is a Banach Space and $M$ is a finite dimensional smooth manifold (for example, the end point map for a control system), what is the strongest ...

**1**

vote

**0**answers

22 views

### Estimates for derivatives of a positive discrete harmonic function

There is the following estimation (Duffin, Discrete potential theory, Theorem 5):
Let $f$ be a discrete harmonic function in a sphere of radius $R$ with the center $p$, all in $\mathbb Z^3$. Then, if ...

**-1**

votes

**0**answers

49 views

### Gradient of the distance function on a manifold [closed]

On a Riemannian manifold, it is known that the function $d(x, p)$, where $p \in M$ is a fixed point, has gradient almost everywhere, with $|\nabla_x d(x, p)| = 1$. Now, if we replace $p$ by an open ...

**1**

vote

**2**answers

147 views

### On the natural density of almost perfect numbers

This question is pretty basic, so I apologize in advance if it is unsuitable for MO. If so, please do let me know and I will migrate it over to MSE.
Essentially, by work of Kanold, we know that the ...

**3**

votes

**1**answer

109 views

### Classification of 3-forms in dimension 7

I'm looking for a classification of $3$-forms over a real vector space of dimension $7$ as for the $3$-forms in dimension $6$. References on the latter case are R. Bryant On the geometry of almost ...

**4**

votes

**1**answer

158 views

### Learning Quantum (Co)Homology and Landau Ginzburg Superpotential

I am learning about Quantum Homology which I have to use in my research, and I see that in many papers (For example in FOOO, "Spectral invariants with bulk, Quasimorphisms and Lagrangian Floer ...

**2**

votes

**2**answers

237 views

### Magnus' embedding theorem

I am looking for a (preferably modern) reference to the following old result of Magnus.
Let $F$ be a free group of finite rank and
$$ F_1 = [F,F], F_2 = [F_1,F_1], \dots , F_{n+1} = [F_n,F_n], \dots ...

**6**

votes

**1**answer

160 views

### Henstock, Differentiation under the integral sign

Does anyone know, where I can find the proof of necessary and sufficient conditions for differentiating under the integral sign in case of Henstock integral? Here are the theorems but not all the ...

**2**

votes

**0**answers

77 views

### Extension of the Hilbert-Mumford Criterion

Let $X$ be a smooth variety, $L$ a line bundle on $X$ and $G$ a reductive group actin on $X$ with a linearization of the action to $L$. Say we are over the complex numbers.
Both the concept of GIT ...

**3**

votes

**0**answers

139 views

### Looking for a copy of Algebraic Number Theory in honor of Iwasawa

I am looking for an electronic copy of this volume:
Advanced studies in Pure Mathematics, Volume 17
Algebraic Number Theory - in honor of K. Iwasawa
Edited by J. Coates, R. Greenberg, B. Mazur and I. ...

**3**

votes

**2**answers

239 views

### How to show the following two definitions of homotopy monomorphism are equivalent?

Let $M$ be a model category. In Toen's The homotopy theory of dg-categories and derived Morita theory Page 11 it is written:
a morphism $x \to y$ in a model category $M$ is called a homotopy ...

**13**

votes

**2**answers

282 views

### Differential operators are coKleisli morphisms of the jet co-monad

The following statement may be "well known but not well known enough", and my question is which reference would state it explicitly:
The construction of Jet bundles is a comonad on suitable bundles ...

**2**

votes

**1**answer

69 views

### Integral kernels of self-adjoint operators [closed]

If the integral kernel $k(x, y)$ of an operator $T : C^\infty_c(M) \to \mathcal{D}'(M)$ is symmetric ($M$ is a compact manifold), then the operator $T$ is symmetric. Is the converse true? That is, ...