Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

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Buchi's conditional proof of the non-existence of finite algorithm to decide solubility of system of diagonal quadratic form equations in integers

I am doing some literature review regarding Buchi's problem. In particular, I am reading the relevant section in this survey paper by Mazur (Questions of Decidability and Undecidability in Number ...
Stanley Yao Xiao's user avatar
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36 views

Generalized envelope theorems

I'm looking for references for two generalizations of Danskin/envelope-type theorems for convex optimization. The first is for when the parameters are functions on a space rather than numbers. A ...
Aaron Bergman's user avatar
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0 answers
126 views

Taking integer values of a sequence of Beurling primes

Let $P=(p_j)_{j=1}^\infty$ be an increasing sequence of real numbers with $1<p_1$ and $\lim_{j\to\infty}p_j=\infty$. As mentioned in [1], Beurling proved that if the multiplicative group $N_P$ ...
Anon12345's user avatar
9 votes
2 answers
632 views

On martingale convergence

Let $(X_t)_{t\ge0}$ be a martingale with continuous paths. It was previously shown here and here that then it is impossible that $X_t\to\infty$ almost surely as $t\to\infty$. Is it possible that there ...
Iosif Pinelis's user avatar
4 votes
1 answer
261 views

Examples of Borel probability measures on the Schwartz function space?

Let $\mathcal{S}(\mathbb{R}^d)$ be the Frechet space of Schwartz functions on $\mathbb{R}^n$. Its dual space $\mathcal{S}'(\mathbb{R}^d)$ is the space of tempered distributions. Minlos Theorem as ...
Isaac's user avatar
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18 votes
1 answer
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Does summing divergent series using cutoff functions give consistent results?

One way to try to give a value $S$ to a divergent series $\sum_{n=1}^\infty a_n$ is with a smooth cutoff function: $$ S = \lim_{N\to\infty}\sum_{n=1}^\infty a_n \eta\left(\frac{n}{N}\right) $$ where $\...
not all wrong's user avatar
5 votes
0 answers
230 views

Video abstracts for mathematical papers

I recently published a video abstract of a manuscript of mine (number theory), finding that more people are interested in its content than when I uploaded the preprint on arXiv. Now, my main question ...
Marco Ripà's user avatar
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3 votes
1 answer
198 views

Weighted Lebesgue space with exponential weights: smoothing effect and properties

I am researching whether there are weighted Lebesgue spaces of the type $$ \left\{ f\omega(x)\in L^p(\mathbb{R}^n):\|f\|_{L^p_\omega}=\int_{\mathbb{R}^n}|f|^p\omega^p(x)\,dx< \infty,\right\} $$ ...
Ilovemath's user avatar
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1 answer
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Is the Fortissimo space on discrete $\omega_1$ radial?

Let $\omega_1$ have the discrete topology. Its Fortissimo space is $X=\omega_1\cup\{\infty\}$ where neighborhoods of $\infty$ are co-countable. A space is radial provided for every subset $A$ and ...
Steven Clontz's user avatar
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Linear third order water wave pde admitting particular gamma factor solution. How do you understand evolution on vertical strip in complex plane?

I would like to understand a little bit about how to interpret and construct $1$-parameter gamma factors that are dynamical - that is they are particular solutions to linear PDE's. Some possible ...
53Demonslayer's user avatar
8 votes
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156 views

An identity for characters of the symmetric group

I am looking for a reference for the identity $$\chi_\lambda(C)=\frac{\dim(V_\lambda)}{|C|}\sum_{p\in P_\lambda,\,q\in Q_\lambda,\,pq\in C}\operatorname{sgn}(q)$$ for the irreducible characters of the ...
Hjalmar Rosengren's user avatar
4 votes
0 answers
124 views

Reference request: Discriminant of a $V_4$-extension of local fields is the product of discriminants of intermediate fields

Disclaimer - cross-posting: I already posted this question on MSE, here. In line with the accepted answer of this meta question, I am also asking it here, since it is a research-level question and it ...
Sebastian Monnet's user avatar
9 votes
1 answer
542 views

Irrationality of cubic threefold (before Clemens and Griffiths)

I came across this notice, which seems to say Fano proved that a general cubic threefold is irrational back in 1940s. I'm interested in seeing this work, especially a proof without intermediate ...
AG learner's user avatar
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1 answer
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The function $G(x) =(4\pi t)^{-d/2} \int_{\mathbb{R}^d} e^{\frac{-|x-y|^2}{4t}}|y|^k dy$ can be controlled when $|x|\rightarrow \infty$

In this paper, Lemma 6, Pinsky proves that $$H(x) =(4\pi t)^{-d/2} \int_{\mathbb{R}^d} e^{\frac{-|x-y|^2}{4t}}(1+|y|)^m \, dy$$ attains its maximum in $x=0$ for $m<0$. This can also be proven using ...
Ilovemath's user avatar
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Decrease of $(1/\zeta)^{(r)}(\sigma + i T)$ as $\sigma\to -\infty$?

What is a standard reference for the simple fact that, for $T$ fixed and $\sigma\to -\infty$, every derivative $|(1/\zeta)^{(r)}(\sigma+i T)|$ of the Riemann zeta function decreases faster than any ...
H A Helfgott's user avatar
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4 votes
1 answer
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Some questions about the definition of Chern classes in Cheeger--Simons differential characters

In page 62 to 63 of the paper "Differential characters and geometric invariants" by Cheeger and Simons, they define, among other things, Chern classes taking values in differential ...
Ho Man-Ho's user avatar
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2 votes
0 answers
475 views

Are these finite semirings known?

I am trying to prove the properties below, and by doing this, I hope to find a way to speed up the computation of the below defined addition and multiplication. I am also interested if these finite ...
mathoverflowUser's user avatar
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0 answers
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Reference needed for powers of semi-group generators

Let $\mathcal{L}$ be the infinitesimal generator of a Markov semi-group. I am looking for references that study powers of $\mathcal{L}$; i.e. $\mathcal{L}^n$, for $n\in\mathbb{N}$. For example, if the ...
matilda's user avatar
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0 answers
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Wondering if Monsky-Washnitzer ever published a result claimed to be forthcoming in a later paper

At the very end of the paper Formal Cohomology I by Monsky and Washnitzer, they write the following: "In some sense, the operator $\psi$ applied to a power series gives it "better growth ...
Vik78's user avatar
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Weighted least squares regression: Iterative modeling of variance

In chemical analysis, the instrument's signal are plotted as a function of chemical concentration. In general, higher the concentration higher is the response and the relationship is linear. At ...
AChem's user avatar
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On characters of the symmetric group: Part 2

This question is related to my earlier MO quest. For an integer partition $\lambda$, denote $\ell(\lambda)=$ length, $\vert\lambda\vert=$ size and $\lambda=$ conjugate of $\lambda$. Allow to write $\...
T. Amdeberhan's user avatar
6 votes
2 answers
634 views

Number of divisors which are at most $n$

I’m interested in the function $\tau_n:\mathbb{N}\to\{1,2,3,\cdots, n\}$ defined by $$\tau_n(x)=\sum_{k=1}^n \mathbf{1}_{k\mid x},$$ the number of divisors of $x$ which are at most $n$. Question 6 of ...
TheBestMagician's user avatar
2 votes
0 answers
209 views

Finding the DOI for a paper

How can we find the DOI of an old paper. For example, what are the DOI of the following papers? Anderson, D.D. and Jayaram, C., 1995. Regular lattices. Studia Scientiarum Mathematicarum Hungarica, 30(...
E.R's user avatar
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0 answers
195 views

A probabilistic proof of van der Waerden theorem

Is there an elementary proof of van der Waerden's theorem on arithmetic progressions using probabilistic methods?
Mohammad Golshani's user avatar
9 votes
1 answer
499 views

Reference request: number of antichains of a partially ordered set

Let $\mathbb{N}$ denote the set of all positive integers. For each $n \in \mathbb{N}$, define the set $$ P_n = \{ (a,b) \in \mathbb{N} \times \mathbb{N} : 1 \leq a \leq b \leq n \} $$ and consider the ...
E W H Lee's user avatar
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1 vote
0 answers
86 views

Reference for a clear version of multigraded Serre-Grothendieck-Deligne correspondence local cohomology

The Grothendieck-Serre-Deligne correspondence states the following. Let $ R $ be a Noetherian, graded ring and let $ T $ be $ \operatorname{Proj}(R) $. If $ \mathcal{F} $ is a coherent sheaf on $ T $...
Schemer1's user avatar
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On Soergel's results concerning projectives modules in category $\mathcal{O}$

I am looking for a translated proof of two results of Soergel usually referred to as endomorphismensatz and struktursatz. Both of those results were shown in the paper Soergel, W. (1990). Kategorie 𝒪...
alerouxlapierre's user avatar
7 votes
2 answers
409 views

On the existence of a real which is not set-generic over $L$

Recall that a real $r$ is set-generic over $L$ if there is a constructible forcing notion $\mathbb{P}$ and some $L$-generic filter $G\subset\mathbb{P}$ such that $r \in L[G]$. I know that Jensen's ...
Lorenzo's user avatar
  • 2,134
0 votes
1 answer
256 views

Factorization trees and (continued) fractions?

This question is inspired by trying to understand the lexicographic sorting of the natural numbers in the fractal at this question: Is $1 = \sum_{n=1}^{\infty} \frac{\pi(p_n^2)-n+2}{p_n^3-p_n}$ , ...
mathoverflowUser's user avatar
3 votes
0 answers
147 views

Defining ideal of a Schubert variety as a kernel

Consider the Plücker embedding of the variety of complete flags in $\mathbb C^n$: $$F_n\subset\mathbb P(\bigwedge\nolimits^1\mathbb C^n)\times\dots\times\mathbb P(\bigwedge\nolimits^{n-1}\mathbb C^n).$...
Igor Makhlin's user avatar
  • 3,493
11 votes
1 answer
686 views

Smooth map between oriented manifolds

Let $f: M\rightarrow N$ be a smooth map between smooth closed oriented connected manifolds of same dimension. Question: is it true that $f$ is smoothly homotopic to some smooth map $g: M\rightarrow N$...
GSM's user avatar
  • 343
2 votes
0 answers
325 views

On characters of the symmetric group: Part 1

Given an integer partition $\lambda$, denote $\ell(\lambda)=$ length, $\vert\lambda\vert=$ size and $\lambda=$ conjugate of $\lambda$. Allow to write $\lambda\vdash n$ either as $(\lambda_1,\dots,\...
T. Amdeberhan's user avatar
2 votes
0 answers
91 views

Are covering families of localizations stable under pushouts?

For a commutative ring $A$, we call a finite family of localizations $A \to A_{S_i}$ (where $S_i$ are some subsets of $A$) a covering if the canonical morphism $A \to \prod A_{S_i}$ is an effective ...
Arshak Aivazian's user avatar
5 votes
1 answer
515 views

Smallest prime factor of numbers

The literature refers to smooth integers as \begin{equation}\Psi(x,y):=\#\{n\le x:P_1(n)\le y\},\end{equation} where $P_1(n)$ is the largest prime factor of $n$. There are lots of results studying $\...
alidixon222's user avatar
17 votes
1 answer
1k views

Explicit character tables of non-existent finite simple groups

In connection with the historical development of the classification of finite simple groups, I am interested in a particular aspect that seems to be less well-documented than the main narrative of ...
Sebastien Palcoux's user avatar
3 votes
3 answers
365 views

Closed formula for number of ones in a proper factor tree

Edit [2023 Dec 7]: One of my specific wonders, along with that of students, is around when a recursive formula might have – or be expected to have – an explicit or closed formula. What is the ...
Benjamin Dickman's user avatar
1 vote
0 answers
122 views

Reference request: unfolding of Integral representation of an L-function

Are there any text or papers that thoroughly address unfolding of integral representation of an L-function such as D. Ginzburg's On Spin L-function for Orthogonal Groups page 762-763 and page 774 (or ...
L-JS's user avatar
  • 151
5 votes
1 answer
123 views

Variants of the Bonk-Schramm embedding

Recently I heard about the following embedding theorem of Bonk and Schramm: every Gromov hyperbolic geodesic metric space with "bounded growth" is roughly similar to a convex subset of $\...
Takao Hishikori's user avatar
2 votes
0 answers
82 views

On dense subspaces of $L^p$-spaces of finitely additive measures

Let $\mu$ be a finite, finitely additive measure defined on the Borel $\sigma$-algebra of a real separable Hilbert space $\mathcal{H}$ with dual $\mathcal{H}^{*}$. Write $L^{p}(\mathcal{H},\mu)$ for ...
S.Z.'s user avatar
  • 463
3 votes
0 answers
210 views

Classifying spaces beyond CW complexes

We know that for a reasonable topological group $G$ (say a compact Lie group) admits a classifying space for $G$-bundles within the category of countable CW complexes. That means, there is a space $BG$...
UVIR's user avatar
  • 971
5 votes
0 answers
131 views

When does an iteration not add functions $\eta\to V$ at the final stage?

I am interested in better understanding the following property: Let us say that an iteration of forcings $\langle\mathbb{P}_\alpha,\dot{\mathbb{Q}}_\beta\mid\alpha\leq\gamma,\beta<\gamma\rangle$ is ...
Calliope Ryan-Smith's user avatar
2 votes
0 answers
89 views

Self adjoint operators from energy functionals

It is known that the equation $$ \Delta f = 0 $$ on some bounded domain $\Omega$ on $\mathbb{R}^n$ subjected to certain boundary conditions can be derived through the minimization of the Dirichlet ...
user8469759's user avatar
4 votes
0 answers
63 views

Pfaffian elements and anomalies

If $X$ is a compact even dimensional spin manifold, then we have a family of chiral Dirac operators parametrized by $Met(X)$, the (infinite dimensional) manifold of Riemannian metrics on $X$. This is ...
domenico fiorenza's user avatar
4 votes
0 answers
244 views

Does there exist research about equation like $u_{tt}=\det(D_{x}^{2}u)+\dots$?

I have asked this question on Mathematics Stack Exchange yesterday, but there still is no reply. Does there exist research about equation like $$u_{tt}=\det(D_x^2 u)+\cdots\text{?}$$ That is to say, ...
monotone operator's user avatar
4 votes
0 answers
87 views

List of equivalent conditions for the invariant subalgebra to be polynomial

Let $k$ be a field, $P_n$ the polynomial algebra in $n$ indeterminates, and $G<\operatorname{GL}_n$ a finite group whose order is coprime to the characteristic of $k$, and that acts on $P_n$ by ...
jg1896's user avatar
  • 2,683
9 votes
0 answers
238 views

Grothendieck purity for Brauer groups of stacks

Let $X$ be a smooth variety over a field $k$ (for the sake of simplicity of characteristic $0$) and $\operatorname{Br}(X) := H^2_{\text{ét}}(X, \mathbb{G}_m)$ its (cohomological) Brauer group (...
Tim Santens's user avatar
7 votes
1 answer
281 views

The origin of a planar graph theorem of Steinitz and Rademacher

The subsequent statements are extracted from the article titled 'Generating r-regular graphs' (https://doi.org/10.1016/S0166-218X(02)00593-0). A well-known classical theorem of Steinitz and ...
L.C. Zhang's user avatar
  • 1,605
8 votes
0 answers
431 views

Does the interior of Pascal's triangle contain three consecutive integers?

This question defeated Math SE, so I am posting it here. Consider the interior of Pascal's triangle: the triangle without numbers of the form $\binom{n}{0},\binom{n}{1},\binom{n}{n-1},\binom{n}{n}$. ...
Dan's user avatar
  • 2,341
3 votes
2 answers
219 views

Abel–Plana formula with fractional offset

The Abel–Plana formula compares the sum $\sum_{n=0}^\infty f(n)$ to the integral $\int_0^\infty f(x)\,dx$, \begin{equation} \sum_{n=0}^{\infty}f\left(n\right)-\int_{0}^{\infty}f\left(x\right)dx=\frac{...
Carlo Beenakker's user avatar
10 votes
1 answer
525 views

Are “most” bounded derivatives not Riemann integrable?

Given $a,b\in\mathbb R$ with $a<b$. Let $$X=\{f\in C([a,b]): f \text{ is differentiable on } [a,b] \text{ with }f' \text{ bounded }\},$$ and $$A=\{f\in X: f' \text{ is Riemann integrable}\}. $$ It ...
Fergns Qian's user avatar

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