# All Questions

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### Question about zeta function of function field in 1 variable over $\mathbb{F}_q$

From my previous question, I know that$$\zeta_X(s) = {{P(u)}\over{(1-u)(1-qu)}}$$for some polynomial $P(u)$ of degree $2g$, where $X$ is the set of all places of $F$, a function field in one ...
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### How many primes have the form $(2^p+1)/3$?

Assuming that $p$ is an odd prime. How many primes have the form $(2^p+1)/3$? Is the number finite? Mathematica calculation shows that there are 23 such primes when $p$ ranges over the first 500 ...
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### Quotient group of an amalgam

If a quotient of a group G is an amalgam then the group G is an amalgam. Is this true or false? How can we describe a quotient of an amalgam?
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### Rational curves through a fixed number of points

Let us fix two positive integers $d$, and $N$. Can we determine a third integer $n$ such that given $n$ general points $p_1,...,p_n\in\mathbb{P}^N$ there exists a unique rational curve of degree $d$ ...
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### When does the free loop space fibration split?

This question is a repost from stack.exchange. It didn't get a lot of attention there. Perhaps it is badly written (or silly?). If so, I'd be happy to get comments/suggestions about that. Let $X$ be ...
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### Concentration and Correlation for Magnitudes of Gaussian Vectors

Suppose we have a large collection of standard normal random variables $a_i\in\mathbb{R}^n$. We know by standard concentration results that if we take $m \geq C\left(t/\epsilon\right)^2n$ samples, ...
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### Generalized Hurwitz Spaces

In this question all the varieties are over $\mathbb{C}$. Classic Hurwitz spaces $\mathcal{H}_{g,r}$ are moduli spaces of simple branched coverings $f \colon X \to \mathbb{P}^1$ of degree $d$, where ...
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### Does the property of being a local homeomorphism descend through split surjections?

Let $f : X \to Y$ and $g : Y \to Z$ be continuous maps (between topological spaces). Assume these hypotheses: $f : X \to Y$ is a split surjection, i.e. has a section. $g \circ f : X \to Z$ is a ...
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### system of linear equations [on hold]

These are the two known equations (I2+I3)-(I1+I4)/(I1+I2+I3+I4) = 2x/L (I2+I4)-(I1+I3)/(I1+I2+I3+I4) = 2y/L where I know x,y,L values. How can I find the values of I1,I2,I3,I4?
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I just found this related question in here Q1. Given a positive definite matrix $\mathbf{A}$, consider its eigendecomposition $(\mathbf{A}\mathbf{V} = \mathbf{V}\mathbf{D})$. Consider an arbitrary ...
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### Oscillating Markovprocess Transition Probabilities

Suppose we have an irreducible positive-recurrent Markov process $\{X(t), t\geq0\}$ with generator $G$. Let $P(t)$ be its transition probability matrix and $\pi$ its stationary distribution. Then we ...
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### Pseudo-braided fusion categories

A few definitions first, please replace with the standard terminology (and correct me if I confuse all the by-names of fusion categories :-) I call a complex number $z$ pseudo-cyclotomic if $|z|=1$. I ...
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### How many Fréchet manifolds are there?

Clearly the title needs clarifying. Allow me to let "how many" to mean a set larger than a skeleton of the category of Fréchet manifolds and smooth maps, if this category is indeed essentially small. ...
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### Two questions about Whittaker functions

I am watching the video: Modeling p-adic Whittaker functions, Part I. I have two questions about Whittaker functions in the video. From 33:00 to 37:00, it is said that after changing of variables, ...
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### Analytic continuation of intertwining operator

I was trying to understand the paper "Form of GL(2) from analaytic point of view", by Gelbart and Jacquet. On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator ...
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### Are genus zero Gromov Witten Invariants on Del-Pezzo surfaces enumerative?

Let $X_k$ be $\mathbb{P}^2$ blown up at $k$ points (where $k$ is $0$ to $8$). Let $\beta \in H_2(X_k, \mathbb{Z})$ be the homology class given by $$\beta := n L + m_1 E_1 + \ldots + m_k E_k$$ ...
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I can't understand log160=log2000+10log(1-r); 2.2041=3.3010+10log(1-r); 10log(1-r)=2.2041-3.3010; 10log(1-r)=-1.10969; ...