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

**9**

votes

**0**answers

237 views

### Letters of a bi-rationalist

V.V. Shokurov has written several papers over the course of about 10 years which are called "Letters of a bi-rationalist". Here are the ones that I could find:
Letters of a bi-rationalist. I. A ...

**8**

votes

**1**answer

668 views

### On the parity of $[x^n]$

I am trying to find a problem which appeared years ago in the American Mathematical Monthly. It went something like this: There was a Putnam Competition question which asked to show that there is a ...

**1**

vote

**0**answers

29 views

### Has anyone used the quincunx dilation matrix to form compactly supported wavelet functions?

Has anyone used the quincunx dilation matrix to form compactly supported wavelet functions? I know that it's possible, in fact a lot of references make the analog of the Harr wavelet basis, but I'm ...

**8**

votes

**1**answer

190 views

### Is there a modern account of Veblen functions of *several* variables?

Veblen $\phi$ functions extend the $\xi \mapsto \phi(\xi) := \omega^\xi$ and the $\xi \mapsto \phi(1,\xi) := \varepsilon_\xi$ functions on the ordinals by repeatedly taking fixed points (I won't ...

**11**

votes

**2**answers

311 views

### Examples of varieties with many automorphisms acting trivially on co-homology

Let $X$ be a smooth projective variety over the complex numbers. Denote by $Aut(X)$ its automorphism group, by $Aut(X)_0$ the connected component of the identity, and by $G$ the quotient ...

**3**

votes

**0**answers

84 views

### State of the art for univariate complex polynomials factorization with algebraic coefficients

Let $\mathbb{K}:=\overline{\mathbb{Q}}$ be the field of algebraic numbers. We choose to represent an element of $\mathbb{K}$ as its minimal monic polynomial, which is a vector in some $\mathbb{Q}^n$.
...

**4**

votes

**0**answers

193 views

### Reference for Hensel's Lemma in Algebraic Geometry

The following form of Hensel's Lemma in Algebraic Geometry is well-documented in the literature:
$\textbf{Theorem 1}$: Let $R$ be an Henselian local ring with maximal ideal $\mathfrak{m}$, and let ...

**0**

votes

**1**answer

162 views

### How to calculate $N_{L/k}$(roots of unity)?

Suppose that $L/k$ is a Galois extension of number fields and that $G$
is the corresponding Galois group. Further, for $\frak p$ a prime ideal
of $\cal O$$_L$, let $K=L^{G(\frak p)}$, where [$L$ : ...

**5**

votes

**2**answers

142 views

### Minimum length of a convex lattice polygon containing k lattice points?

Let $f(k)$ denote the minimum length of a convex lattice polygon containing exactly $k$ lattice points (including lattice points on the boundary).
It is not too hard to show that $k = \frac{1}{4\pi} ...

**4**

votes

**1**answer

265 views

### On the complexification of a Riemannian manifold

Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle. If we suppose $TM\otimes\mathbb{C}$ is the complexification of $TM$ then how can we define a natural metric on the complex bundle ...

**6**

votes

**0**answers

204 views

### Topological entropy and periodic sequences of a subshift

Let $\Sigma$ be a two-sided subshift on a finite alphabet $A$. Let $\Sigma_n$ denote all words $x_{-n}\dots x_n\in A^{2n+1}$ such that $(x_k)_{-\infty}^\infty \in \Sigma$ for some $x_k, |k|>n$.
...

**1**

vote

**0**answers

38 views

### Continuity of Busemann-Hausdorff area density

I am trying to find out why the Busemann-Hausdorff area density as defined by Burago and Ivanov is continuous. Here, $GC_m(V)\subset \Lambda^m(V)$ denotes the simple $m$-vectors in an $n$-dimensional ...

**9**

votes

**1**answer

110 views

### Cross between the nil-Hecke ring and the group ring of a Coxeter group

A Coxeter system $(W,S)$ has a set of generators $S=\{s_1,s_2,\ldots\}$ and the Coxeter group $W$ is determined by relations of the form $(s_is_j)^{m_{ij}}=1$ for some integers $m_{ij}$, where ...

**8**

votes

**1**answer

257 views

### Have the explicit Poisson-type formulas of Guinand and Meyer been observed before?

In a recent paper of Meyer Measures with locally finite support and spectrum PNAS vol. 113 no. 12:3152–3158 (behind a paywall, but see also these seminar notes) some new explicit Poisson-type formulas ...

**8**

votes

**0**answers

242 views

### Has it been proved that odd perfect numbers cannot be triangular?

(Note: This question has been cross-posted from MSE.)
Euclid and Euler proved that every even perfect number is of the form $m = \frac{{M_p}\left(M_p + 1\right)}{2}$ where $M_p = 2^p - 1$ is a prime ...

**0**

votes

**0**answers

41 views

### Brunett Derrida behaviour for the branching brownian motion with selection

In this paper Berard and Gouéré proved that for a binary branching random walk with selection of the N rightmost particles the cloud of particles moves asymptotically at a deterministic velocity ...

**1**

vote

**0**answers

25 views

### Constructing the external map to a polynomial-like map [closed]

I am reading the paper by Douady and Hubbard, On the Dynamics of Polynomial-Like Mappings, and I am at a loss to understand a crucial step in the construction of the right domain for finding the ...

**5**

votes

**1**answer

124 views

### Quantum group representations from (convolution) matrix units?

Let $A=F(\mathbb{G})$ be the algebra of functions on a finite quantum group with a Haar state $$h=:\int_\mathbb{G}:F(\mathbb{G})\rightarrow \mathbb{C}.$$
There is a convolution product on ...

**5**

votes

**0**answers

89 views

### Complex L^1 spaces; reference request

I have been doing a fair amount of research into a complex analytic modified version of the Mellin transform. I have hit a few roadblocks, and am hoping there may already be literature on the subject. ...

**7**

votes

**2**answers

263 views

### Thompson group $V$

R. Thompson introduced three groups $F\subset T\subset V$. The question concerning amenability of $F$ is still unanswered and has attracted much attention. I have read that Thompson group $V$ contains ...

**8**

votes

**1**answer

228 views

### Tube of a mod p point on a smooth Z_(p)-scheme

Let $R$ be a smooth, integral, finite-type $\mathbb{Z}_{(p)}$-algebra of relative dimension $n$ and $\overline{f} \colon R \to \mathbb{F}_p$. Then Hensel's lemma tells us that this lifts to a map $R ...

**0**

votes

**0**answers

59 views

### Sobolev function and capacity

It seems that there is a theorem which claims that
If $u\in L_1^2(B_1\setminus T)$ and $T\subset B_1$ is of capacity zero (in some sense, since the author says $(1,2)$-capacity, of which I don't ...

**3**

votes

**1**answer

205 views

### Examples of topological dynamical systems with countably infinitely many ergodic invariant measures

Suppose a discrete group $\Gamma$ acts on a connected compact metrizable space $X$ by homeomorphisms. Denote such a topological dynamical system by $(X,\Gamma)$.
Question: is there any $(X,\Gamma)$ ...

**3**

votes

**2**answers

98 views

### Algorithms for Sorting Subset Sums

In this question the number of unique sortings has been discussed.
As a follow-up, I would like to know, whether the problem of sorting the sequence of subset sums has ever been studied.
There ...

**4**

votes

**1**answer

266 views

### what is the injective hull of indecomposable module of preprojective algebra

Let $Q$ be a ADE type quiver and $s_i$ ($i$ runs through the vertices of $Q$) be the simple $\Lambda$-module with 1-dimensional vector space at vertex $i$ and zero-dim at other vertices. Here ...

**4**

votes

**0**answers

67 views

### Cases of equality in Daykin's theorem

Let $A$ and $B$ be sets of subsets of $\{1, \dots, n\}$, and let $A \wedge B = \{a \cap b : a\in A, b\in B\}$, $A\vee B=\{a\cup b: a\in A, b\in B\}$. Then
$$
|A \wedge B| |A\vee B| \geq |A||B|,
$$
as ...

**3**

votes

**0**answers

62 views

### Invariant Lagrangians of a connection and its derivatives: how do they look like?

Let
$$
L=L(\Gamma,\partial\Gamma,\ldots,\partial^n\Gamma)
$$
be a Lagrangian depending on a linear symmetric connection $\Gamma$ on the tangent space of a manifold $M$ together with its derivatives up ...

**0**

votes

**0**answers

58 views

### Extremum of the cyclic sum of polynomial ratios (same degree)

I've noticed a few times (probably nothing new) that cyclic sums (assuming $x, y, z > 0$) like:
$\frac{x^2+y^2}{yz} + \frac{y^2+z^2}{zx} + \frac{z^2+x^2}{xy}$,
where in each of the 3 ratios, all ...

**1**

vote

**1**answer

119 views

### Neat definition of Harris Ergodicity

I can't find any reference where the definition of Harris Ergodicity for Continuous time Markov processes is defined.
a) What would be exactly the definition?
b) What reference could be helpful?
...

**4**

votes

**1**answer

213 views

### Reference request, proof about well-ordering of ordinals

I am looking for a second order proof that ordinals are well-ordered up to $\epsilon_0$.
So, starting with encoding those ordinals in numbers, defining the < relation on those encoded ordinals and ...

**5**

votes

**1**answer

172 views

### When two vertex (operator) algebras can be patched-up to a full CFT on a genus 0 surface?

Theorem 3 of the nLab article "Full field algebra" states that
Theorem 3. Two vertex operator algebras $V$ may appear as the left and right chiral halfs of a full conformal field theory precisely ...

**3**

votes

**1**answer

94 views

### Menger's Theorem for planar triangulations

I was reading the paper "Planar separators" by Alon, Seymour and Thomas (available on the first author's webpage). They consider a planar triangulation, that is, a maximally planar graph $G$ drawn in ...

**5**

votes

**1**answer

158 views

### Rigid analytic geometry in characterstic 0 vs positive characteristic

This question is motivated purely by curiosity. In algebraic geometry there is a major distinction between the world of characteristic $0$ and that of characteristic $p > 0$ with different methods, ...

**4**

votes

**1**answer

81 views

### The minimum number of Hamiltonian paths in a strongly connected tournament of order $n$

For $n\ge3$ let $a(n)$ be the minimum number of Hamiltonian paths in a strong (i.e., strongly connected) tournament of order $n.$
Where is $a(n)$ discussed in the literature? Is the exact value ...

**1**

vote

**0**answers

53 views

### Polarization of the Prym variety

Let $X\rightarrow Y$ a ramifield double cover of curves, $J_X, J_Y$ their jacobians, $P\subset J_X$ the Prym variety, for any line bundle $L$ on $X$ of degree $g_X-1$, denote by $\Theta_L$ the ...

**1**

vote

**2**answers

85 views

### A Lie-like product in rings with involution

Suppose $R$ is a ring with involution $*$ and $x,y\in R$. Does the quantity $xy-y^{*}x^{*}$ have a standard name? Has this product undergone systematic study in the ring-theory literature, and if so, ...

**1**

vote

**2**answers

45 views

### List of tensor product spaces with uniform crossnorms

Let $H^{(j)}$ and $G^{(j)}$ be Banach spaces for $j\in\{1,\dots,n\}$. Call norms $\|\cdot\|_{H}$ and $\|\cdot\|_{G}$ on the algebraic tensor products
$H:=\bigotimes_{j=1}^n H^{(j)}$ and ...

**7**

votes

**0**answers

210 views

### A “direct” proof that hyperbolic groups are not amenable

I am looking for a proof that a finitely generated hyperbolic groups is non-amenable [unless it is virtually cyclic] which is as "metric/combinatoric" as possible.
Here are the two proofs I am aware ...

**8**

votes

**2**answers

396 views

### $L^\infty-L^2$ smoothing for heat equation on manifold using Nash-Moser-De-Giorgi technique

Let $M$ be a compact and closed smooth Riemannian manifold, and consider weak solution $u$ of the equation
$$u_t - \Delta u = f$$
given $f \in L^2(Q)$ and $u(0)=u_0 \in L^\infty(M)$.
I'm looking for ...

**1**

vote

**0**answers

57 views

### Norm-averaging reference request

(Apology in advance for the broadness of this question) I recently came across a relatively simple application where I needed to "balance" the "spreaded-out-ness" of a function with the "peaked-ness" ...

**0**

votes

**0**answers

132 views

### Structure theorem for non-Noetherian local rings

Is there a structure theorem (like Cohen 's structure theorem) for non-Noetherian local rings?
I am adding what I am looking for as someone asked in the comment.
If $R$ is a local domain (not ...

**4**

votes

**1**answer

189 views

### Eisenstein Series on Siegel Space

I am looking for any reference dealing explicitly with Eisenstein series on Siegel space (the simplest case of $\rm{SP}_4$ is fine). Anything would be welcome, but in particular I'm interested in the ...

**6**

votes

**1**answer

119 views

### Lowest index giving half of the sum

Numbers $x_1,x_2,\ldots,x_n$ are drawn independently and uniformly from the interval $[0,1]$. Order them as $y_1\ge y_2\ge\dots\ge y_n$, and let $S$ be their sum. Let $k$ be the smallest index such ...

**5**

votes

**0**answers

130 views

### Push forward of the constant sheaf for a Serre's fibration

Let $f\colon X\to Y$ be a proper continuous map of topological spaces which is a Serre's fibration. $X$ and $Y$ may be assumed to be locally compact, $Y$ is connected topological manifold of finite ...

**2**

votes

**0**answers

36 views

### Largest disk inside a spherical domain

It is known (Pestov-Ionin theorem) that if $k_{max}$ is the maximum curvature of a smooth planar loop $\gamma$, then there is a disk of radius $1/k_{max}$ inside $\gamma$. I wonder is there any ...

**3**

votes

**1**answer

110 views

### Do all non-degenerate quadratic forms come from positive even lattices?

Let $(G,+)$ be a finite Abelian group. We say $q\colon G\to \mathbb{T}$ is a non-degenerated quadratic form, if $q(-a)=q(a)$ and the symmetric function
$$
b(g,h) =q(g+h)q(g)^{-1}q(h)^{-1}
$$
is a ...

**6**

votes

**1**answer

194 views

### Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible

Let $\mathbb A = (A, +_A)$ be a cancellative, but possibly non-commutative, monoid with identity $0$, and fix an element $x \in A$. Does there always exist a cancellative monoid $\mathbb B = (B, +)$ ...

**1**

vote

**2**answers

154 views

### Where can I find some articles and lecture notes in renorming theory in Banach spaces? [closed]

I am really into renorming theory in Banach spaces especially, renorming in non-reflexive Banach spaces such that they have nice property, for example they have fixed point property,locally uniformly ...

**2**

votes

**1**answer

652 views

### Reference for Connes Bourbaki membership or otherwise

Alain Connes being a leading French mathematician today one could ask whether he is a member of the Bourbaki group. Is there a published reference that would either refute or confirm this?

**1**

vote

**0**answers

78 views

### Reference: Relative cohomology of a morphism

Let $f\colon Y \to X$ be a morphism of schemes, the inverse image in $K$-theory always fit into a long exact sequence
$$
\cdots \to K_i(f)\to K_i(X) \xrightarrow {f^*} K_i(Y)\to \cdots
$$
where the ...