# All Questions

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### Normal basis with cyclotomic units

Let p be an odd prime integer and let $\zeta$ be a primitive p-th root of unity. Let $\alpha$ be a non-trivial cyclotomic unit of $\mathbb Q(\zeta)$, i.e. an element of the form ...
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### Proof that no differentiable space-filling curve exists

Could someone provide a reference or a sketch of a proof that no differentiable space-filling curve exists? Or piecewise differentiable? Must every continuous space-filling curve be nowhere ...
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### Question on homogeneous measures

Let $\mu$ be a strictly positive measure ($m(a)=0$ iff $a=0$) on a Boolean algebra $B$. $\mu$ is called homogeneous if it have the same Maharam type on every $b\in B$. By additive measure algebra I ...
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### Existence of a “quasi-uniform” probablility distribution on $\mathbb{Z}$

Does there exist a probability distribution on $\mathbb{Z}$ such that for every integer $n\geq 1$, the probability that a random integer $x$ is divisible by $n$ equals $1/n$? Henry Cohn has an ...
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### “Gross-Zagier” formulae outside of number theory

The Gross-Zagier formula and various variations of it form the starting point in most of the existing results towards the Birch and Swinnerton-Dyer conjecture. It relates the value at $1$ of the ...
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### Lindelöf subsets of $P$-spaces

A completely regular topological space $(X,\tau)$ is called a $P$-space, if every $G_\delta$-subset of $X$ is open. (i.e $\tau$ is closed under countable intersection). Here we recall some special ...
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assuming we have two smooth function ${f_1},{f_2}:{R^N} \to R$, under what condition, we have ${f_1}\left( {{{\bf{x}}_1}} \right) \ge {f_1}\left( {{{\bf{x}}_2}} \right) \leftrightarrow ... 1answer 68 views ### Representability of deformation functors via SGA I'm trying to understand Böckle's proof of Theorem 2.1.1 in his notes on deformation theory. Let's start with some motivation. Let$\Gamma$be a profinite group (I'm thinking of an absolute Galois ... 3answers 747 views ### “Epicycles” (Ptolemy style) in math theory? By analogy: The epicycles of Ptolemy explained the known facts in the sun system and in this sense were not "wrong". But they distracted from a better insight. From another viewpoint, everything fell ... 1answer 292 views ### Size of KL-divergence neighbourhoods I am new here. I was reading another post here and this got me wondering what can be said about the size of the following kl divergence neighborhoods. Consider these two kl-divergence neighbourhood ... 0answers 37 views ### how can i calculate the 2x2x2 (doublet tensorproduct) [on hold] help me the simple question how can I calculate the doublet@doublet@doublet @ : tensor product please teach me 2answers 52 views ### Moment problem for discrete distributions Let$x_1, \dots, x_N \in \mathbb R$and consider the discrete distribution$\mu := \frac{1}{N} \sum_{i=1}^N \delta_{x_i}$, where$\delta_x$denotes the Dirac measure, i.e. for any measurable set$B ...
In a recent theorem we have naturally come across this condition, that seems to be important, but rarely satisfied: $\sqrt{\frac 1 4 + a^m} \in \mathbb Q(\zeta_m, a)$ where $a\in\mathbb C^*$ and ...