# All Questions

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### Non-reflexivity of $B(\mathbb H)$

How does one prove that the space $B(\mathbb H)$ of bounded operators on a infinite dimensional (separable) Hilbert space is not reflexive? I guess this should go along the lines of the ...
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### Are RKHS separable?

If I consider some reproducing kernel Hilbert H space with kernel K(x,y), is this Hilbert space separable? In particular, if my feature space X is separable, I think that I may find an Hilbert basis ...
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### On the Riemann's theorem [on hold]

What's the philosophy behind the Riemann's theorem, if it becomes true that: for $n\neq 1$ and $i= 1$, and, for $s$ is any complex number, such that, ...
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### can all CM types be realized by Jacobians?

The question is kind of self contained, but let me develop a bit further. Assume K is a CM field of degree $2g$, that is, a quadratic imaginary extension of a totally real field. A CM type of $K$ is ...
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### Supersolvablity of groups

Wath are the equivalent conditions for Supersolvablity of a group? Specially biprimary groups?
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### Is there an efficient algorithm to solve ECDLP over global field?

Let E be an elliptic curve over $\mathbb{Q}$. Is there an efficient algorithm which can solve an elliptic curve discrete logarithm in E?
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### SU(2) Lefschetz decomposition for cohomology of Riemann surface Jacobian

Start with a closed Riemann surface with $g$ handles $\Sigma_g.$ I'm interested in the cohomology of its Jacobian $Jac(\Sigma_g)=T^{2g},$ in particular how the $SU(2)$ or $SL(2,\mathbb{R})$ Lefschetz ...
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### Open cell decomposition after applying a Weyl group element

Let $G=\operatorname{GL}(n,\mathbb C)$. What follows can be put into a more general context, but I would like to first understand it for this case, the generalization is a second step. For ...
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### Numbers with disjoint sets of multiples of integer parts

Let $\alpha>0$ and define $S(\alpha)=\{\lfloor n \alpha \rfloor: n\in\Bbb Z^+ \}$. (Here $\lfloor x\rfloor$ is the integer part of $x$ and $\mathbb Z^+$ the set of positive integers.) Is there any ...
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### On the equation $a^n + b^n = c^2$

I am interested in the possible natural solutions of the equation $a^n + b^n = c^2$ where $n \geq 4$ is fixed. I am not sure if it is well-known or not, so any suggestion would be helpful.
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### Bounding the perimeter of a geodesic triangle in spaces of non-positive curvature

This is probably an easy question, but I don't know any Riemannian geometry and a literature search hasn't helped. Any help (e.g. providing a reference) would be greatly appreciated. For a triangle ...
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### function equation with translation of independent variable [on hold]

The following has come up in some work I'm doing: If $f(x+a)/f(a)=g(x)$, where $g(x)$ is given and $a\geq0$ is a constant, what is $f(x)$? We can assume that $g(x)>0, \forall x$. Of course a ...
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### Basis of free quotients of free groups

Let $F$ be a finitely generated free group. Consider $R\subset F$ a finite set of relations and denote with $G$ the quotient group of $F$ by the normal closure of $R$. Now suppose we are given ...
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### Real cusp forms

Most literature on modular functions (invariant or covariant with weight k under the full modular PSL_2(Z) group) treats holomorphic functions and introduce the notion of cusp forms (modular functions ...
myThe definition of the Euler characteristic (given in Guillemin and Pollack's "Differential Topology") of a compact oriented manifold $X$ is the self-intersection number of the diagonal $\Delta$ in ...