0
votes
0answers
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
votes
0answers
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
votes
0answers
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
0answers
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
votes
0answers
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
1answer
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
0answers
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
1answer
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
2answers
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
1answer
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
2answers
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
votes
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
1answer
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
0answers
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
2answers
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
1answer
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
96 views

Talking about the abc-conjecture [on hold]

What is the latest news about the abc-conjecture?
8
votes
1answer
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
1answer
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
0answers
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
1answer
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
1answer
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
0answers
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
0answers
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
2answers
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
0answers
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
0answers
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
0answers
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
3answers
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 ...

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