# All Questions

98,609 questions
945 views

### Complex analytic vs algebraic geometry

This is more of a philosophical or historical question, and I can be totally wrong in what I am about to write next. It looks to me, that complex-analytic geometry has lost its relative positions ...
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### A continuous inverse function problem: search for an inconsistent theory approach to return a 'false' metric [on hold]

My problem is about metrizable space definition: I need to find a topology that can be described by a metric without this being, in fact, a 'true metric'. I search an alternative approach to avoid to ...
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### Number of compositions of a positive number n, with factors between 1 and a certain number m

I'm trying to find the number of compositions of a positive number n, with factors between 1 and a certain number m. That is, all the combinations of limited numbers that add up to n $f(n, m)$ For ...
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### In search of a new isometric twisting invariant $T= \tau_1.\tau_2$

A curved line in $\mathbb R^3$ has properties of curvature and torsion, and, on an $\mathbb R^2$ possesses surface scalar properties of normal curvature and geodesic torsion $(\kappa_n, \tau_g).$ ...
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### analyze existence limit of sin(sqrt(x)) in infintiy [on hold]

i'm studying to test and i found a problem from last years: analyze the existence of limit $$sin(\sqrt x)$$ in infinity. Got some ideas about argument tending to infinity, but its especially hard for ...
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### On certain 2 dimensional foliation of $Gl(2,\mathbb{R})$ deleted by scalar matrices

We consider the following 4 dimensional open manifold $$M=Gl(2,\mathbb{R})\setminus \{\lambda I_2 \mid \lambda \in \mathbb{R}\}$$ where $I_2$ is the identity matrix. We consider the $2$ dimensional ...
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### Is a matrix similar to its transpose over $\mathbb{Z}_p$?

Is every $n \times n$ matrix with entries in $\mathbb{Z}_p$ (or even $\mathbb{Z}$) conjugate to its transpose via a matrix in $GL_n(\mathbb{Z}_p)$? On the one hand, I know the analogous fact is false ...
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### My question is about an article concerning p and t [on hold]

you say concerning p and t: An example of an element of p is the family of sets (indexed by k∈ℕ) defined by {m to the power of k :m∈ℕ}. But the second condition is not met because the set {2 to the ...
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### Relate solutions to a polynomial system in complex numbers to solutions in a finite field

Suppose I have a system of polynomials which are homogeneous but of distinct degrees that I want to solve simultaneously: $$F_1(z_1,\ldots,z_n)=\cdots=F_m(z_1,\ldots,z_n)=0.$$ Let $X(\mathbb F)$ ...
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### Fargues's Theorem for $Spa(C,C^+)$ (rather than $Spa(C,O_C)$

$\DeclareMathOperator\Spa{Spa}$Fargues's Theorem for $\Spa(C,O_C)$ states that the category of (mixed characteristic) shtukas with one paw at $x_C$ is equivalent to the category of Breuil-Kisin-...
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### Growth rate of bounded Lipschitz functions on compact finite-dimensional space

Let $\mathcal X$ be a metric space of diameter $D$ and "dimension" (e.g doubling dimension) $d$. Let $L \in [0, \infty]$ and $M \in [0, \infty)$ and consider the class $\mathcal H_{M,L}$ of $L$-...
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### Products of Cyclotomic Polynomials with Nonnegative Coefficients

I'm curious if there are any results that allow us to determine if a product of cyclotomic polynomials (not necessarily all distinct) results in a polynomial having nonnegative coefficients. Some ...
284 views

### Is there a short proof of the decidability of Kepler's Conjecture?

I've believed that the answer is "yes" for years, as suggested in various sources with reference to Tóth's work. For example, the Wikipedia article for Kepler Conjecture says: The next step toward ...
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### Potential for a Monotone Operator

[Cross-posted from math.stackexchange] I have a question about understanding the proof of Theorem 4.11 in the paper A Potential Theory for Monotone Multivalued Operators (accessible here). The ...
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### Reference for Shalika germs of GL(n)

I was reading the two Repka papers where he computes the leading and subleading Shalika germs for $GL_n$ and I was wondering, where are we since then? Have these germs (and the integrals) been ...
I am interested in the question above. I know that the answer is NO if the base field is for instance $\mathbb{Q}$ (the intersection of $\mathbb{Q}(x^2)$ and $\mathbb{Q}((x-1)^2)$ is $\mathbb{Q}$ ...