1
vote
0answers
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
vote
1answer
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
1answer
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
votes
0answers
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
0answers
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
0answers
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
2answers
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
votes
0answers
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
2answers
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
0answers
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
0answers
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
1answer
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
votes
0answers
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
1answer
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
votes
0answers
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
vote
0answers
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
votes
1answer
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
votes
0answers
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
0answers
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
2answers
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
votes
0answers
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
vote
0answers
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
0answers
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
vote
0answers
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
0answers
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
votes
0answers
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
1answer
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
vote
0answers
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
1answer
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
votes
1answer
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
1answer
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
votes
0answers
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
2answers
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
vote
0answers
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
0answers
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
vote
0answers
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
vote
0answers
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
1answer
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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
1answer
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
1answer
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
1answer
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
0answers
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
0answers
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
1answer
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
0answers
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 ...

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