# All Questions

**0**

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13 views

### Is the fundamental group of an open arithmetic Riemann surface contained in $\Gamma(2)$

Let $X$ be a non-compact Riemann surface with universal covering $\mathbb H$ and suppose that the fundamental group of $X$ is an arithmetic subgroup of $\mathrm{Aut}(\mathbb H) = ...

**0**

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**0**answers

12 views

### Direct integral (in automorphic forms)

1.) The right regular representation $R(g)$ of $Gl_2(\mathbb{A})$ on the Hilbert space $$L^2(Gl(2,\mathbb{Q})/\ Gl(2, \mathbb{A}))$$ decomposes as a direct integral, written $$\int ...

**0**

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**0**answers

45 views

### How to solve $e^{f(x)} + a f(x) + bx = 0$

How should determine solutions to equations of this form?
$$e^{-f(x)} + b f(x) = ax$$
Here $f(x)>0$ is real valued. Also $a>0$, $b>0$.

**1**

vote

**0**answers

27 views

### Finite extension of K(x) with extra structure: definable over field of invariants?

Let $K$ be an algebraically closed field, and let $\sigma$ be an automorphism on $K$. Set $k=K^\sigma$. Consider the rational function field $K(x)$ and extend $\sigma$ to $K(x)$ by $\sigma(x)=x$, ...

**-4**

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**0**answers

20 views

### How to solve the following integral [migrated]

Do you have any idea how to solve the following integral:
$\int\limits_0^a {{e^{ - \frac{{by}}{{c - dy}} - ey}}dy}$,
where $a$, $b$, $c$, $d$ and $e$ are constants?
Thank you very much.

**2**

votes

**1**answer

28 views

### Finite series with reciprocal factorials

I asked the question at MSE
http://math.stackexchange.com/questions/982388/simple-finite-series-with-reciprocal-factorials
but got no answer or comment (it is not a homework).
I'm trying to find the ...

**3**

votes

**0**answers

112 views

### Any counterexamples known for the Generalized Tate conjecture?

One can state the generalized Tate conjecture over arbitrary finitely generated fields; to this end one should just define Galois representation to be effective if the eignevalues of the actions of ...

**1**

vote

**1**answer

20 views

### Polynomial (non-)embedding of a simplex in euclidean space

Let $\Delta$ be a standard $k$-simplex, and let $f:\Delta\to\mathbb R^N$ be a polynomial map with known numerical coefficients. What sort of practical computational algorithms can be used to ...

**5**

votes

**2**answers

163 views

### $j$-invariants of elliptic curves over finite fields

Let $K$ be a finite field, and $\overline{K}$ its algebraic closure. It is well known that two curves are isomorphic over $\overline{K}$ if and only if they have the same $j$-invariant. If two such ...

**5**

votes

**1**answer

445 views

### Is every number the sum of two cubes modulo p where p is a prime not equal to 7?

If p is a prime other than 7, can every integer be written as sum of two cubes modulo p?
Has Waring's problem mod p for cubes been proved simply and directly?
Thanks for your proof.
Lemi

**4**

votes

**2**answers

109 views

### Which groups are LERF?

A finitely generated group $G$ is called LERF if every finitely generated $H \leq G$ is closed in the profinite topology on $G$ (equivalently, there is a family of finite index subgroups of $G$ ...

**0**

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**0**answers

49 views

### 2x3 = 5+1 AND 2+3 = 5x1. How many other examples of this type? [migrated]

I noticed the following:
2x3 = 5+1.
If you switch the operators, it is still true:
2+3 = 5*1.
There is another obvious/trivial example where you can swap the operators:
2x2 = 2+2.
I think these ...

**3**

votes

**0**answers

36 views

### Reference for a fact (?) on homeomorphic knot complements

Does somebody have a reference (or an argument why it should be true) for the following statement?
“Let $K$ and $K'$ be knots in $S^3$. If there is an orientation-preserving homeomorphism $h : S^3 ...

**1**

vote

**0**answers

14 views

### How to infer missing nodes from a path?

I have a first data set which is a list of train stops with coordinates (lat, lon), but not the "links" between the nodes/stops (this could thought of as a null or empty graph).
I have a second data ...

**2**

votes

**0**answers

62 views

### Marshall Hall's theorem for surface groups

Let $\Gamma_g$ be a surface group of genus $g \geq 2$, that is we have a presentation: $$\Gamma_g = \langle x_1,y_1 \dots, x_g,y_g \vert \prod_{i = 1}^g [x_i,y_i] = 1\rangle$$
Let $H \leq \Gamma_g$ ...

**2**

votes

**1**answer

181 views

### Doing some homological algebra in triangulated categories

It's well known that chain complexes are an abelian category, and in particular we can consider chain complexes of chain complexes, i.e. double complexes. Given a double complex $A^{\bullet\bullet} ...

**0**

votes

**1**answer

26 views

### Existence of half-planes with respect to regular open sets of the Euclidean plane

I initially asked this question at math.stackexchange.com but there was no reaction, so I thought this may be a good idea to transfer it to mathoverflow.net
Let ...

**10**

votes

**0**answers

66 views

### When is a group Fibonacci sequence contained in a single conjugacy class?

First a definition: a Fibonacci sequence in a group is a sequence in which the first two elements may be arbitrary, and from there on each element is a product (using the group operation) of the ...

**3**

votes

**2**answers

91 views

### Topological characterization of injective metric spaces

Let $\ (X\ d)\ \,(Y\ \delta)\ $ be arbitrary metric spaces. A function $\ f:X\rightarrow Y\ $ is called a metric map (with respect to the given metrics $\ d\ \delta$) $\ \Leftarrow:\Rightarrow\ ...

**1**

vote

**1**answer

37 views

### Does restriction to an open subgroup preserve projective smooth representations?

Let $G$ be a locally profinite group and $K \le G$ an open subgroup. Does the restriction functor $\mathrm{Res}^G_K$ from the category of smooth $\mathbb{C}$-linear representations of $G$ to smooth ...

**1**

vote

**0**answers

17 views

### Central automorphisms of groups act transitively on Krull-Schmidt decompositions

(Cross posted from math.SE)
I'm looking for a modern reference to the subject line, preferably one that doesn't use Ore's generalizations to modular lattices.
To clarify terminology...
Suppose we ...

**8**

votes

**0**answers

72 views

### Reinhardt cardinals and iterability

Work in $ZF$. Let $j:V\to V$ be a non-trivial elementary embedding which is iterable, so that we can iterate it and form models $M_\alpha, \alpha\in ON,$ with $M_0=V,$ and elementary embeddings ...

**1**

vote

**1**answer

62 views

### Name for (function, set) pairs?

Right now I'm working on a topological graph theory problem. To prove a theorem I introduced some objects. Has anyone heard of something similar before? I would like to call them by the right name.
...

**0**

votes

**0**answers

25 views

### Nonlinear ODE system

Let $\Psi(a) = \frac{a}{2}$ if $a>0$ and $0$ if $a\le 0$.
Now we consider the following coupled system of nonlinear ODEs:
$$\begin{aligned}&\frac{1}{2}\sigma_1^2 u_1''(x) + \mu_1 u_1'(x) + ...

**-2**

votes

**0**answers

37 views

### Particular case of every sequence has a Cauchy subsequence? [on hold]

A metric space (X,d) has the following property:
Given $\epsilon >0$ and non-empty finite subset $X_\epsilon \subset X$
$$ \inf \{ d(x,p) : p \in X_\epsilon \} < \epsilon$$
I would like to ...

**2**

votes

**1**answer

73 views

### Compact induction as a tensor product

Let $G$ be a locally profinite (i.e., locally compact Hausdorff and totally disconnected) topological group, $H \le G$ a closed subgroup, and $(W, \sigma)$ a representation of $H$ over $\mathbb{C}$ ...

**2**

votes

**0**answers

49 views

### Lattice model for Affine Grassmannians of non type A

There is a Lattice model for affine Grassmannians of type A, due to Lusztig. It describes affine Grassmannians of type A as the moduli space of certain subspaces in an infinite-dimensional ...

**-1**

votes

**0**answers

40 views

### Sequence of cosine converges? [on hold]

Does the following sequence
$$(\cos (\pi \sqrt{ n^2 + n}))_{n=1}^\infty $$
converge?
Can I use the ratio or root test?

**-1**

votes

**0**answers

51 views

### Bolzano-Weierstrass application? [on hold]

I am having problems proving the following claim:
Given a bounded set $A \subset R^n$, I want to prove the existence of $a_1, \dots, a_N \in R^n$ and numbers $r_1, \dots, r_N \in [0, +\infty)$ such ...

**7**

votes

**0**answers

88 views

### Countable choice in $L(\mathbb{R}^*_G)$

Let $\lambda$ be a singular strong limit cardinal and let $G \subset \text{Col}(\omega,\mathord{<}\lambda)$ be a $V$-generic filter. Let $\mathbb{R}^*_G = \bigcup_{\alpha < \lambda} ...

**4**

votes

**1**answer

255 views

### How to visualise Bollobas' 1965 theorem?

Theorem
$[n]=\{1,\ldots,n\}$. Let $\lbrace (R_i, S_i), i \in I \rbrace, R_i, S_i \subset [n]$ be such that $R_i \cap S_i = \emptyset, R_i \cap S_j \ne \emptyset (i \ne j)$. Then $$\sum_{i \in I} ...

**0**

votes

**0**answers

27 views

### how to compute bergman kernel

i have a question to determin if the asyptotic expansion of Bergman kernel has a log term. Is there anyone can show me is there any general way to tell?

**-1**

votes

**0**answers

9 views

### How to best fit for linear vs sinusoidal curve [on hold]

I have to analyze a series of data points for my environmental science class, but I've never taken statistics. I want to determine whether a line or sinusoidal curve (with a very large period -- ...

**0**

votes

**0**answers

63 views

### Solving matrix equation (AX)^2+(BY)^2=D [on hold]

Is there any method that can solve the matrix equation in such a form (AX)^2+(BY)^2=D? A and B are matrix, X, Y and D are column vectors. (Solve for X and Y)
I originally have two equations such as ...

**1**

vote

**0**answers

74 views

### Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems:
Let $f(x)$ be a convex funtional ...

**2**

votes

**0**answers

48 views

### Computing Euler Charactistics of Line bundles on Hilbert Schemes of points on Surfaces

Let $S^{[2]}$ be the Hilbert scheme of two points on a smooth projective surface (actually, right now I am particularly interested in del Pezzo surfaces). Let $B$ be the exceptional divisor of the ...

**0**

votes

**1**answer

108 views

### Free action of symmetric groups

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?
Is there a compact manifold which can be act freely by all symmetric ...

**-5**

votes

**0**answers

96 views

**8**

votes

**1**answer

169 views

### How do I check that this is a Frobenius algebra?

Let $f_1,f_2,\ldots,f_n\in \mathbb C[z_1,\ldots, z_n]$ be such that the quotient ring
$$A:=\mathbb C[z_1,\ldots, z_n]/(f_1,f_2,\ldots,f_n)$$
is finite dimensional (in other words, it's a ...

**1**

vote

**1**answer

48 views

### Special retraction from a metric space onto an arc

Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ ...

**0**

votes

**0**answers

41 views

### Sequence from count [on hold]

I need to generate a formula for a programming project. The formula will assist in the positioning of elements on screen.
I would like a formula that produces the following sequence indefinitely:
1, ...

**0**

votes

**1**answer

68 views

### Braids, pure braids and Dehn twists

Consider the braid group with $n$ strands $B_n$. Each braid can be drawn (say) from bottom to top as $n$-intertwining strictly monotonic strands. Moreover, the group $B_n$ is generated by $n-1$ ...

**10**

votes

**1**answer

141 views

### Diffeomorphisms and homotopy equivalences sliced over BO(n)

There are some classical results stating sufficient conditions on a manifold $\Sigma$ such that every homotopy equivalence $\Pi(\Sigma) \stackrel{\simeq}{\longrightarrow} \Pi(\Sigma)$ is homotopic to ...

**-2**

votes

**0**answers

77 views

### Prove irrationality for the supplied exercise [on hold]

How can I prove that the product of cube root of 2 and the cube root of 4 is irrational ?
3 sqrt(2) * 3 sqrt(4) = irrational.
Thanks!

**3**

votes

**0**answers

56 views

### Annihillator of the highest weight vector in a finite-dimensional representation

Let $\mathfrak g$ be a simple complex Lie algebra and let $V(\lambda)$ be a finite-dimensional representation with highest weight $\lambda$. Let $v$ be the highest weight vector. Then the action of ...

**2**

votes

**2**answers

108 views

### Question on Posets and open sets

i'm sorry if my question is really trivial but this one is really bugging me out..
So let's have a partially ordered set $I$ with the topology in which the open sets are the increasing ones: $i\in U$ ...

**4**

votes

**0**answers

69 views

### Intersections in almost complex manifolds

Main question: Suppose $(M,J)$ is an almost complex manifold, and $X$ and $Y$ are two almost complex submanifolds (i.e. $J(T(X)) \subset T(X)$ and $J(T(Y)) \subset T(Y)$). Then must $X \cap Y$ also be ...

**0**

votes

**0**answers

37 views

### decomposition of polynomials over a field [on hold]

$K|F$ has this property that every polynomial $f(x)∈F[x]$ has a root in $K$.is it true that every polynomial $f(x)∈F[x]$ can be completely decomposed on $K$?
i think it is false,because if we write ...

**-5**

votes

**0**answers

28 views

### How to find secret key and public key for ECC cryptosystem? [on hold]

Develop an ECC cryptosystem based on E31(1;1),
point G = (0,1) which has order 32.
nA value of 6.
What is the secret key?
What is the public key?

**0**

votes

**3**answers

62 views

### On the existence of compactly supported functions whose its Fourier transform satisfies a given condition

My question is concerned with the existence of compactly supported functions whose its Fourier transform satisfies a given condition: For $\gamma\ge 1$, one can prove that there is no compactly ...