# All Questions

9 questions

**5**

votes

**0**answers

142 views

+300

### Find a condition such that the spectral radius for a special matrix is smaller than 1 (or a matrix norm smaller than 1)

We need a help to find a reasonable condition such that the spectral radius for a special matrix $\mathbf{J} \otimes\hat{\mathbf{G}}\hat{\mathbf{W}} + \mathbf{I}\otimes\mathbf{\hat{H}}$ is smaller ...

**0**

votes

**0**answers

382 views

+50

### Conjectured primality tests for specific classes of $k\cdot b^n \pm 1$

Can you provide proofs or counterexamples for the claims given below?
Inspired by Lucas-Lehmer-Riesel primality test I have formulated the following two claims:
First claim
Let $P_m(x)=2^{-m}\...

**22**

votes

**1**answer

636 views

+100

### Intuitive reason why the $j$-invariant is a cube?

Let $\tau$ be a CM point of discriminant $D$. Assume that $D$ is not divisible by $3$. Then $j(\tau)$ is an algebraic integer of degree equal to the class number $h(D)$. Let $ \gamma_2(\tau)=j(\tau)^{...

**9**

votes

**0**answers

111 views

+200

### Kazhdan-Lusztig equivalence for Lie super-algebras

Let $\mathfrak g$ be a semi-simple Lie algebra. Kazhdan and Lusztig studied the category of representations of the corresponding affine Lie algebra (the central extension of $\mathfrak g((t))$) which ...

**2**

votes

**1**answer

205 views

+50

### Meaning of Alberti rank-one theorem

Heuristically what does Alberti's rank-one theorem imply about the structure of a $\mathrm{BV}$ vector field $\boldsymbol{b}$?
Is it rigorously fair to say that the level lines of $\boldsymbol{b}$ ...

**0**

votes

**0**answers

69 views

+100

### Some confusion about weights and roots in parabolic root systems

I was reading James Arthur's book An Introduction to the Trace Formula and had a couple of questions. Here $A_0$ is a maximal split torus of a reductive group $G$, $P_0 \supset A_0$ is a minimal ...

**8**

votes

**1**answer

138 views

+50

### Nonabelian finite groups with “locally commuting” presentation

Let $G = \left\langle S | R \right\rangle$ be a finitely presented group where S is a set of generators and R is a set of relations. We say that the presentation is "locally commuting" if whenever two ...

**4**

votes

**0**answers

199 views

+200

### A strong plus-one hypothesis

To make this more easily readable, I'll start with the question and then give the explanation/motivation.
Question. Is the following principle (or its weakening, with "for every real $r$" replaced ...

**0**

votes

**0**answers

55 views

+50

### Bifurcations due to a nonlinearity parameter

Suppose we want to analyze the behavior of the system
$$\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x},t;\varepsilon),\quad \mathbf{x}\in\mathbb{R}^n,\quad t\in\mathbb{R}^+,\quad\varepsilon\in\mathbb{R}^+,
$$
...