# All Questions

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### Lower regularity version of Moser's theorem on volume elements

A theorem of Moser, published in "On the Volume Elements of a Manifold" (Transactions of the Americal Mathematical Society 120, 1965), shows that if a $C^\infty$ compact manifold $M$ has two ...
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### Cramer's theorem in Hilbert spaces

I am interested under what conditions Cramer's theorem applies in random variables taking values in Hilbert spaces. Following these lecture notes, but using a Hilbert space: Let $X_1,X_2,\cdots$, be ...
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### How to compute $\pi_{3}$ of $L(p,q)\# L(p',q')$?

Let $L(p,q)$ be a 3-dimensional lens space, and let $L(p',q')$ be another. Is there any known result concerning the 3rd homotopy group of the connected sum $L(p,q)\# L(p',q')$? If not, I am interested ...
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### Mathematically compute - species diversity [on hold]

Using a simple model, and having these as paramters numberofspecies <- 100 meaninitialpopulationsize <- 50 sdloginitialpopulationsize <- 1 #determines variation in initial population ...
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### Representations of $\text{SL}(n,\mathbb{F}_p)$ and $\text{Sp}(2n,\mathbb{F}_p)$ whose dimensions are $p^k$

I should preface this by saying that I am not a representation theorist, so I apologize if this can easily be found in standard sources (but sadly I cannot seem to extract it from any of the books I ...
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### Odds of 7 straight spins on a roulette wheel falling within the same group of 12 numbers [on hold]

What are the odds of 7 straight spins on a roulette wheel rendering a number within the same group of 12 numbers? (i.e. 7 numbers within 1-12, 7 within 13-24 or 7 within 25-36). This would be a ...
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### Construct the best piece-wise linear continuous function fitting given curve

How to construct the optimal piece-wise linear continuous function fitting given curve and given number of knots (optimal knots positions also must be determined by this method)?
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### A conjectural convergence condition for a weakened Elliott-Halberstam conjecture

For $a$ and $q$ positive integers such that $a\lt q$ and $(a,q)=1$, let $\pi(x;q,a)$ be the number of primes $p\equiv a\pmod q$ below $x$. One can show that $\pi(x;q,a)\sim \dfrac{\pi(x)}{\varphi(q)}$ ...
Assume that $f_1$ is the first eigenfunction of the Dirichlet Laplacian $-\Delta f = \lambda f$, $U=\{z\in \mathbf{C}:|z|<1\}$ and $f|_{|z|=1}=0$. Assume also that $\lambda_1$ is the first ...
Suppose that $G$ is a topologically finitely generated profinite group and $H$ is a subgroup of countably infinite index. Can I say that $H$ must be topologically finitely generated with the subspace ...