# All Questions

**1**

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122 views

### Coefficients of $f(t)=(\sum_{m=0}^{+\infty}e^{2\pi im^4t})(\sum_{m=0}^{+\infty}e^{2 \pi inm^4t})$

I want to prove that $\forall n \in \mathbb{N}$ at least one of the Fourier coefficients of $f(t)=(\sum_{m=0}^{+\infty}e^{2\pi im^4t})(\sum_{m=0}^{+\infty}e^{2 \pi inm^4t})$ is striclty greater than ...

**1**

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**1**answer

254 views

### Are chain complexes over a field always injective?

Question: Let $\mathbb{F}$ be an algebraically closed field of characteristic zero and let $\mathrm{Ch}_{\mathbb{F}}$ be the category whose objects are chain complexes (of $\mathbb{F}$-modules) and ...

**1**

vote

**1**answer

196 views

### Confusion with proof about a fact $\mathbb{P}$-name [on hold]

Let $\mathbb{P}$ be poset.
Let $B$ be a set. We say that a $\mathbb{P}$-name $\dot{b}$ is a nice name for member of $B$ if there is a maximal antichain $A\subseteq\mathbb{P}$ and a function ...

**-1**

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**0**answers

28 views

### How to prove an inequality $\left| {g(j + 1)} \right| \le 5/4$ in Stein's method for Poisson approximation [migrated]

The following is a lemma in
Barbour, A. D., Holst, L., & Janson, S. (1992). Poisson approximation. Oxford: Clarendon Press,p7.
For $j=1,2,...$ and $\lambda > 0$, we have
$\left| {g(j + ...

**1**

vote

**0**answers

82 views

### About real roots of complex multivariable polynomials

Say we have a function $f : \mathbb{C}^{n+1} \rightarrow \mathbb{C}$ such that,
$f(z,w_1,w_2,..,w_n) = \prod_{k=1}^{q} (z - a_k) = A_i(w_i-b_i)(w_i-c_i) $ where the $a_i$ are known to be real for ...

**3**

votes

**0**answers

115 views

### Prime zeta zeros - reference

Is there an online repository for zeros of the prime zeta function? I looked at the Yahoo group
Prime numbers and primality testing listed on the MathWorld notebook for the prime zeta function, but ...

**4**

votes

**2**answers

402 views

### Based loop groups as stacks?

I have been stuck for some time, thinking about the following question.
Let $G$ be a Lie group. Its classifying space $BG$ can be seen as the differentiable stack $[pt/G]$, which is of dimension ...

**-1**

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**0**answers

183 views

### What is the error here? [on hold]

Let $X$ a curve of genus $g\geq 3$ with a double cover to an elliptic curve $Z$. Let $F$ be a rank $2$ and degree $1$ locally free sheaf on $Z$, and $G$ its pullback to X.
Then, by Serre duality ...

**7**

votes

**2**answers

305 views

### What is the Hausdorff dimension of this fractal?

Let $\sum_{i=h}^\infty d_i/b^i $ be the base $b$ representation of $x \geq 0,$ where $b>1$ and the $d_i$ are uniquely determined by the greedy algorithm. For fixed $c>1,$ let $f(x)= ...

**-1**

votes

**0**answers

18 views

### Simulate correlated random field of probabilities [on hold]

Hi I am trying to simulate a spatial latent random field that are probabilities not correlated binary data as specified in other posts. The goal is to have the probabilities correlated by distance. ...

**0**

votes

**0**answers

62 views

### On a property of split short exact sequences [migrated]

Let $A_{\bullet}, B_\bullet$ and $C_\bullet$ be three short exact sequences of groups (not necessarily abelian) out of which $A_\bullet$ and $B_\bullet$ are split. Assume that there is again a short ...

**5**

votes

**1**answer

111 views

### Rademacher average based Hoeffding Inequality

I am following these lecture notes:
Given the i.i.d. $\mathcal{Z}$-valued random variables $Z_1,\dotsc,Z_m$ and $\mathcal{G}$ is a set of bounded functions $g\colon \mathcal{Z}\to[a,b]$.
Corollary ...

**0**

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**0**answers

108 views

### Torsion in cohomology

Suppose to have a short exact sequence of chain complexes of $\mathbb{Z}$-modules:
$$0\to A^\bullet\to B^\bullet\to C^\bullet\to 0$$
such that $A^k,B^k,C^k$ are non zero for $k=0,1,2$.
Moreover, ...

**2**

votes

**1**answer

164 views

### Loop space structures on $RP^\infty$

I am interested in infinite loop structures on the infinite dimensional projective space $\mathbb{R} P^\infty$. Is it unique? I think this has to be known in work of May, and If so, then I presume its ...

**-3**

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**0**answers

72 views

### Proalgebraic completion [on hold]

For a finitely generated group, say Γ, what is the meant by of the proalgebraic completion of Γ? I came across this while seeing a paper on Representation Growth for Linear Groups by Larsen and ...

**1**

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**0**answers

64 views

### Are all (graded) Artinian complete intersections like this?

I'm trying to prove some stuff (it's not important what) about (graded) Artinian complete intersections $R=\mathbb{C}[x_1,\ldots,x_n]/I$, where the $x_i$ have certain positive weights and where $I$ is ...

**10**

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**1**answer

411 views

### A group whose automorphism group is cyclic

Is there an Abelian group $A$ which is not locally cyclic whose automorphism group is cyclic ?
This question was first posted here.

**-4**

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**0**answers

40 views

### Pumping Lemma CFL [on hold]

L={ab^n ab^n ab^n: n ≥ 0}
I've just started learning pumping lemmas, but this one confuses me. How can I show that this is not context free?

**-5**

votes

**0**answers

43 views

### Enumeration, selective intersect labs(::) [on hold]

{2,3,4,5::1,5,6,8::3,4,5,6}
2×3×4×5=120
1×5×6×8=240
3×4×5×6=360
(561×8=(234×5)+(156×8)+(345×6))
Preorder to 4488(yπ+) at (2345+1568+3456)/3.141592653...:
4+4+3+3=2+3+4+5
4+4+3+3+2+2=3+4+5+6
...

**5**

votes

**2**answers

236 views

### Combinatorial designs textbook recommendation

Good evening, I am currently taking a class which has combinatorial designs as the first topic, we are using Peter Cameron's book Designs, Graphs, Codes and their Links which I am finding extremely ...

**5**

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**0**answers

68 views

### How to characterize the class of $(\mathfrak{g},K)$-modules with a fixed lowest K-type in the framework of D-modules?

Let $G$ be a real semisimple Lie group, $K$ be a maximal compact subgroup. Let $\mathfrak{g}_0$ and $\mathfrak{k}_0$ be their real Lie algebras respectively. Let $\mathfrak{g}$ and $\mathfrak{k}$ be ...

**1**

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**0**answers

66 views

### “Exceptional components” of the exceptional divisor of a blow up

Assume we are blowing up an ideal $I$ on an affine variety $X$, let $E$ be the exceptional divisor, and $P$ be a (closed) point in $V$, the zero set of $I$. Is there any algorithm to check that $E$ ...

**-2**

votes

**0**answers

96 views

### Existence and local compactness of the p-adic number field without Axiom of Choice [on hold]

I think we can prove the existence and local compactness of the p-adic number field without using Axiom of Choice. Am I right?

**1**

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**0**answers

31 views

### Techniques for finding the stationary state of a continuous-state, discrete-time Markov process

I'm interested in a continuous-state, discrete-time Markov process. Let the distribution at time $t$ be $f_t(x)$. The update equation has the form
\begin{equation}
f_{t+1}(x) = \int f_t(x') g(x', x) ...

**0**

votes

**0**answers

93 views

### Anticommuting operators with positive properties

Which classes of $M\in \mathsf M_k(\Bbb R)^{n\times n}$ admit solutions $N\in \mathsf M_k(\Bbb R)^{n\times n}$ such that
$$(M\otimes N+N\otimes M)(u\otimes u)=0$$ forall $u\in \mathsf D_k(\Bbb ...

**3**

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**0**answers

23 views

### Quasi-M matrices?

Does any body know a reference on lower triangular matrices with negative entries everywhere except for the diagonal and subdiagonal where entries are positive (when all entries are negative with ...

**14**

votes

**1**answer

307 views

### Number of solutions to equations in finite groups

Suppose $G$ is a finite group and that $E$ is an equation of the form $x_1 x_2 ... x_n = e$, where each $x_i$ is in the set of symbols $\{x, y, x^{-1}, y^{-1}\}$.
Is it always true that the number ...

**1**

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**0**answers

66 views

### Degree 2 curves on a degree d hypersurface in P^(2d+2)/3

One of the foundations of Gromov-Witten theory is the use (due to Kontsevich I think) of localization to calculate the number of degree $n$ curves on a general quintic 3-fold. When calculating the ...

**6**

votes

**1**answer

227 views

### Find a polynomial not in any ideal generated by polynomials of total degree $o(n)$

Is there an explicit nontrivial (= not a constant) polynomial $p \in \mathbb{C}[x_1, \ldots, x_n]$ such that, for any ideal $I \not= \mathbb{C}[x_1, \ldots, x_n]$ generated by $f_1, f_2, \ldots, f_m$ ...

**3**

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**1**answer

115 views

### reference for “curves over S are locally the base change of a curve over S' which is finite type over R”

So recently I heard someone claiming that if $X\rightarrow S$ is a smooth curve (not necessarily proper?) and $S$ is an arbitrary scheme over $\text{Spec }R$ (for $R$ sufficiently nice), then there is ...

**6**

votes

**1**answer

71 views

### Chains of forking extension in stable theories

Let $T$ be an stable theory.
Further we work in the monster model of $T^{eq}$.
We say that a chain of types of the form
$$tp(a_1/A_1)\subset tp(a_2/A_2) ... \subset tp(a_n/A_n)$$
is a forking chain ...

**6**

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**0**answers

63 views

### Must nonunit in group algebra of free group generate proper two-sided ideal?

Let $F$ be a free group and $k$ be a field. If $x$ is an element of
the group algebra $k[F]$ that is not a unit (equivalently, that is not
a nonzero scalar multiple of an element of $F$), must the ...

**3**

votes

**2**answers

195 views

### A question on the effective cone

Let $X$ be a projective variety and $G$ a finite group acting on $X$. We consider the quotient $\pi:X\rightarrow Y :=X/G$.
I'm interested in the relation between $Eff(X)$ and $Eff(Y)$. In ...

**1**

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**0**answers

15 views

### Compactness of Weyl pseudodifferential operators with integrable symbols

Given a tempered distribution $s \in \mathcal{S}'(\mathbb{R}^{2d})$, define the Weyl pseudodifferential operator of symbol $s$ as the mapping $\mathcal{S}(\mathbb{R}^{d}) \rightarrow ...

**-4**

votes

**0**answers

55 views

### Theory of Numbers. PROOF using division algorithm and well ordering theorem [on hold]

I really help with the following two questions.
1) Assume that b>0. Show that there exists k an element of Z, s.t a+kb>0. (Use the division algorithm)
2)Use Theorem 3.8 (well ordering theorem) to ...

**1**

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**0**answers

78 views

### Best constant for Maier's theorem?

Maier proved that, for fixed $\lambda>1,$
$$
\limsup_{x\to\infty}\frac{\pi(x+\log^\lambda x)-\pi(x)}{\log^{\lambda-1}x}>1
$$
and in particular
$$
\limsup_{x\to\infty}\frac{\pi(x+\log^\lambda ...

**1**

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**0**answers

57 views

### Normal bundles of rational equivalent curves

Let $C_1, C_2$ be rationally equivalent curves in a smooth projective variety $P$. Let $$N_i: = \mathcal{H}om(I_{i}/I^2_{i}, \mathcal{O}_{C_i})$$ be the normal bundle of $C_i$, where $I_i$ is the ...

**3**

votes

**1**answer

35 views

### Subsets of sets of positive Hausdorff dimension with controlled upper Minkowski dimension

Call a Borel set $A \subseteq [0,1]$ good if $$0 < \dim(A) \leq \overline{\dim_\text{M}}(A) < 2 \dim(A),$$ where $\dim(A)$ is the Hausdorff dimension of $A$ and $\overline{\dim_\text{M}}(A)$ is ...

**-4**

votes

**0**answers

199 views

### Mathematical urban legend - Best second tier mathematician [on hold]

A few years ago I heard a story about a talk given at Stanford by a famous probabilist, perhaps Kai-Lai Chung. The speaker got into some sort of argument with a mathematician in attendance, and called ...

**4**

votes

**1**answer

139 views

### liftings of principal bundles

I would like to know what structure has the category of liftings of a principal bundle. Let me be more precise.
Fix $k$ an algebraically closed field and $X$ a smooth projective variety over it (for ...

**-2**

votes

**0**answers

78 views

### Weak Foundation in Math [on hold]

I read this article http://www.xamuel.com/five-ways-to-be-better-at-math/ and was wondering if anyone can help me with references or advice to get better at math. I always considered myself weak at ...

**2**

votes

**0**answers

74 views

### Adding a row to a Young Tableau via Novelli-Pak-Stoyanovskii

Let $T_{\lambda}$ be the set of standard young tableaux (SYT) of shape $\lambda_1\geq \lambda_2\cdots\geq \lambda_n$. Now consider pushing a row $\mu$ with $\mu\geq \lambda_1$ onto $Y$ to give shape ...

**2**

votes

**0**answers

66 views

### Deformation with fixed ramification

Suppose that $f : X \to Y$ is a finite, surjective morphism of normal varieties. I want to know about the space of first-order deformations of $X$ over $Y$ with fixed ramification, i.e. the ...

**0**

votes

**1**answer

76 views

### Intersection multiplicty and global sections

Let $X$ be a smooth projective variety, $V, W$ closed subschemes in $X$ such that $V \cap W$ is finitely many points. Let $\mathcal{L}$ be a line bundle on $X$. Is there any relation between ...

**1**

vote

**1**answer

60 views

### About preserving real-rootedness of multivariable polynomials

Say $f_i(z_1,z_2,..,z_m)$ are polynomials real rooted in the $z$s for a bunch of polynomials indexed by $i$. When can one say that $\sum_{i} p_i f_i(z_1,z_2,..,z_m)$ is also real rooted?
If ...

**0**

votes

**1**answer

61 views

### Is there an irreducible subfactor with an infinite homogeneous single chain lattice?

We know that we can build an irreducible subfactor realizing a finite single chain lattice containing any finite index irreducible maximal subfactors, by using the free composition (see here).
Is ...

**0**

votes

**0**answers

33 views

### Finding a random variable with a density function [on hold]

So I have this homework I'm having a really hard time starting:
For the random variable X with density function
f(x) =
4x , 0 < x ≤ 1/2
4 − 4x , 1/2 < x ≤ 1
0 , otherwise
Determine the ...

**0**

votes

**0**answers

24 views

### Problem implementing Ramez algorithm [on hold]

I'm implementing the Ramez algorithm for optimal polynomials, and I'm having problems. That is, I'm getting worse and worse approximations.
Repo: https://github.com/nmiculinic/dismat2[1]
Viewer: ...

**2**

votes

**1**answer

125 views

### Is this structure a Banach bundle?

Let $X$ be a Banach space. Put $Y=\{ \phi\in X^{*}\mid\;\; \parallel \phi \parallel\leq 1\;\; \&\;\; \phi \neq 0\}$ which is a locally compact Hausdorf space with the weak star topology.
...

**0**

votes

**0**answers

27 views

### normality of truncated arc space

Let $X=Spec(A)$, with $A$ a normal $k$-algebra of finite type, $k$ is a field.
For any integer $n$, let $X(k[t]/(t^{n}))$ the $n$-th truncated arc space, is it also normal?
Same question for ...