# All Questions

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### Irreducible polynomials with a root modulo almost all primes

Let $f \in \mathbb{Z}[x]$ be a non-zero polynomial which is irreducible over $\mathbb{Q}$. Suppose that $f$ has a root in $\mathbb{F}_p$ for almost all primes $p$. Must $f$ be linear? ...
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### compute the automorphism of Iwasawa manifold

An Iwasawa manifold is a compact quotient of a 3-dimensional complex Heisenberg group by a cocompact, discrete subgroup. We can also refer to Griffiths and Harris's Principles of Algebraic Geometry ...
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### Relation between the eigenvalue density and the resolvent?

Disclaimer: This is a cross-post from Math Underflow. Given that there is little activity on the subject (random-matrice) on the aformentioned site, and given that many interesting discussion on this ...
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### Finding special vectors generated by a matrix

Let $G\in \Bbb Z^{n\times n}$ be an unimodular matrix. Are there any efficient algorithms to find maximum norm of vector $v$ that satisfies $\langle\Delta(v),v\rangle=0$ over all vectors $v\in xG$ ...
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### The Theory of Transfinite Diophantine Equations [on hold]

The theory of Diophantine equations is one of the main stream research areas in number theory. There are many known results and unknown conjectures about the existence of non-trivial solutions for ...
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### Maximal Submodule of a Verma Module

Let $\mathfrak{h}$ be a Cartan subalgebra of a $\mathbb{C}$-semi simple Lie algebra $\mathfrak{g}$. Given $\lambda \in \mathfrak{h}^*$, $M(\lambda)$ the Verma module of highest weight $\lambda$ and ...
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### hyperbolic orbifolds of small area

Is there a list of 2-dimensional hyperbolic orbifolds obtained from reflection groups (such as the double of a hyperbolic triangle with angles $\pi/p$, etc.) of small area, for instance area smaller ...
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### Monotonicity properties of Poisson distributions

During my current research [on inventory management policies, i.e., something really applied ;-) ] I am trying [since quite some time already] to prove a certain monotonicity result for Posson ...
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### The type of nondefinable elements-2

Consider a countable transitive model $\mathfrak{M}$ of set theory. Let $X$ be a definable collection of sets of reals. My question is: is the type of nondefinable elements in $X$ is definable over ...
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### What is the significance of the Spec of non-affine structure sheaf sections?

Let $X$ be a scheme and let $U \subseteq X$ be an open subset of $X$. If $U$ is an affine chart, then $\mathrm{Spec}(\mathcal{O}_X(U)) = U$. Suppose now that $U$ is not an affine chart. By this, I ...
I've read that Kahane and Salem show that if $\mu$ is any measure supported on the ternary Cantor set, then $\hat{\mu}(\xi) \not\to 0$ as $|\xi| \to \infty$, however I have been unable to find a ...
Let $X$ be a manifold such that $dim(X)=n$. It is well-know that if $\mathcal{F}$ is a coherent sheaf $H^m(X,\mathcal{F})=0$ for all $m >n$ (where I denote with $H(-)$ Cech cohomology). But is ...