# All Questions

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### Computing Gauss Legendre Curvature for Large N

I've been scanning across the web, and haven't found a good method to compute the Gauss Legendre abscisas and weights $\{ x_j, w^j \} _j$ for large N. My question is how to do it, and why should it ...
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### One question on complex analysis about analytic functions

Let $\Omega$ be a bounded planar domain and let $O_1, O_2$ be two open subsets of $\Omega$ such that their closures are disjoint. Let $\mathcal{A}$ be the class of analytic functions on $\Omega$, is ...
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### a Theory of Iterated Functions

I'm an amateur who's looking for a co-writer to publish articles relating to the question below and others, derived from a general result applicable to topics as diverse as prime or random numbers, as ...
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### How to teach generalizing the induction hypothesis?

I just finished teaching a class on using proof assistants (in this case, Agda) to write provably correct programs. Reflecting on how it went, the biggest difficulty I noticed the students having was ...
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### Restriction of locally free sheaves and semi-stability on curves

Let $C$ be a stable curve and $\mathcal{F}$ be a locally free sheaf on $C$ such that the restriction of $\mathcal{F}$ to any of the irreducible component $C_i$ of $C$, $\mathcal{F}|_{C_i}$ is Gieseker ...
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### Multivariable function analysis

Sorry if the terms I'm going to use is not professional enough:) This is about the complexity analysis of an algorithm. Let $\alpha$ be the largest zero root of the polynomial ...
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### Analogues of the Monster for central charges different from 24

One way to define the Monster group is to consider a conformal field theory (CFT) corresponding to central charge $c=24$ and look at the automorphism group of its vertex operator algebra. For one of ...
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### the associated action on the transition functions

Let $X$ be a curve with an involution $\sigma$ generically unramified, given a $G-$bundle $E$ of rank $r$, than we ca take its pull-back, I want to describe the action of $\sigma$ on $G$. Fix a ...
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### Probabilistic proof for expander existence [on hold]

I am new to probabilistic proofs and trying to understand them better. Apparently, a common probabilistic proof focuses on the existence of expanders (eg. vertex expanders). I've been using the search ...
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### Rellich's theorem from compact resolvent

On a compact Riemannian manifold, we know that the Laplacian $\Delta$ has compact resolvent. In proving this, one typical way is to use Rellich's theorem about the compact embedding of $H^1(M)$ into ...
SO it is known that Titchmarsh S function $$S(T)= \pi^{-1} arg\quad \zeta\bigg(\frac{1}{2}+iT\bigg)$$ under the assumption of riemann-hypothesis gives $$S(T)=O(\frac{\log T}{\log \log T})$$ can ...