Newest Questions
162,027 questions
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Applicability of Besicovitch Covering Theorem in different norms in $\mathbb{R}^n$
This question is probably quite simple, but I would still appreciate a straightforward answer, whether positive or negative. Thank you in advance.
I alredy know that the Besicovitch Covering Theorem ...
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Kashiwara-Schapira Stack of microsheaves
I will assume familiarity with the notions of singular support as defined by Kashiwara and Schapira in Sheaves on Manifolds. Let $M$ be a manifold, one can define a functor :
$\mu Sh^{pre} : Op_{T^*M, ...
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Hyperplane sections of general type surfaces
Let $X$ be a smooth projective complex surface with $K_X$ very ample. Let $D\in |K_X|$ be a general element.
Does there exist another smooth projective variety $D'$ with a finite flat morphism $D\to D'...
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Dirichlet series of $\zeta'(s)\zeta'(1-s)$
I want to find the Dirichlet series coefficients of $\zeta'(s)\zeta'(1-s)$.
I know that $$\zeta'(s)=-\sum_{n=1}^{\infty}\frac{\log n}{n^s},$$provided $\Re(s)>1$. I would have thought it would be ...
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Expected number of steps for a random walk to return with a single barrier
Here is the problem and a possibly noobie question I am trying to figure out.
You have a biased random walk on $\mathbb{Z}$ with jump to the left probability $p=0.7$ and jump to the right $q=1-p=0.3$. ...
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What is known about the algebras $\mathrm{End}_{U_q(\mathfrak{sl}_2)}(L(d)^{\otimes n})$?
Let $A_{d,n}=\mathrm{End}_{U_q(\mathfrak{sl}_2)}(L(d)^{\otimes n})$. For $d=1$, this is the Temperley-Lieb algebra $A_{1,n}=TL_n(q+q^{-1})$. For $d=2$, Scrimshaw calls this the tangle algebra, first ...
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Nonnegative submartingales: convergence to infinity in probability
Consider a nonnegative submartingale $X_n$, with uniformly bounded jumps, and jump variance uniformly bounded from below. Can we conclude that it converges to infinity in probability? Also, is it ...
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Categorical structure guaranteed to exist, but not necessarily preserved
Background
I'm currently studying arithmetic universes (AUs), which are defined to be list-arithmetic pretoposes (see "Joyal's arithmetic universe as list-arithmetic pretopos" by Maietti). ...
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For endorsement [closed]
I am a research scholar working in the area of General Topology, and I would like to submit it to arXiv under the math.GN category. As this is my first submission in this category, I need an ...
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Algorithm that allows to get any value of A000123 if finite number of values of A002577 are known
Let
$T(n,k)$ be an integer coefficients such that $$ T(n,k) = \begin{cases} 1 & \text{if } k = 0 \vee n = k \\ \displaystyle{ \sum\limits_{i=k-1}^{n-1} T(n-1,i) T(i,k-1) } & \text{otherwise} \...
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Combining two Dirichlet polynomials into one polynomial
I want to write $$\sum_{m_1,m_2\le M}\frac{a(m_1)}{m_1^s}\frac{a(m_2)}{m_2^{1-s}}$$ as one single Dirichlet polynomial that is, I want to find the Dirichlet polynomial $\sum_{n\le N}f(n)n^{-s}$ such ...
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Factorization of polynomials vanishing on quadrics: divisibility by the defining equation
Let $P(x,y,z)$ be a real polynomial that vanishes on the ellipsoid defined by $$ g(x,y,z) := \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} - 1 = 0.$$ How can one rigorously justify the ...
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Equivalent definitions of volume of representations (or characteristic classes of flat bundles)
Statement of the problem:
Let $M$ be a closed connected oriented manifold with fundamental group $\Gamma$ (considered as covering transformations acting on its universal cover). Let $G$ be a (...
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Circle action on free loop space of a classifying space
It is a folklore result that if $G$ is a discrete group and $BG$ its classifying space, then the free loop space $L(BG)$ is homotopy equivalent to $EG\times_{Ad} G$ where $EG$ is the universal $G$-...
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A structured recursive formula for the complete homogeneous symmetric polynomial
I recently discovered a recursive, closed-form summation formula that appears to compute the complete homogeneous symmetric polynomial $h_n(x_0, x_1, \dots, x_{m-1})$, but in a more structured and ...
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