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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References for the computation of the Mordell-Weil group of an elliptic curve

I am reading about the Mordell-Weil group of an elliptic curve over a number field using primarily Silverman's AEC. While the book is excellent in discussing materials prior to Chapter 8, I think ...
Shreya's user avatar
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2 votes
0 answers
130 views

Looking for the multiplicity-free paper by N.Inglis

I'm looking for the paper "Multiplicity-free permutation characters, distance-transitive graphs and classical groups, PhD Thesis, University of Cambridge, 1986" by Nicholas Francis John Inglis. The ...
LeechLattice's user avatar
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9 votes
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A characterization of root systems via their intersections with halfspaces

In a recent preprint I obtained a nice characterization of root systems as a side product. I can imagine that this was known before, and that a source for this statement can shorten the proof of my ...
M. Winter's user avatar
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4 votes
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142 views

Alternative definitions of Weibel's homotopy K-theory

Consider a sort of $\mathbb{A}^1$-homotopy-stable algebraic $K$-theory for rings constructed as follows. For $K_0$ we take a symmetrization subject to natural direct sum operation of $\mathbb{A}^1$-...
Kolya Ivankov's user avatar
5 votes
1 answer
318 views

Diagonal of a diagram of codescent objects

Given the following diagram in a $2$-category, in which squares of the same "type" commute, where each column and each row is a strong codescent diagram (Edit: it should be reflexive as well), is ...
Martin Brandenburg's user avatar
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2 answers
528 views

On Exercise 2.5.10 in Ram. M. Murty's book, "Problems in Analytic Number Theory."

I have just been told about this result, available as Exercise 2.5.10 in Ram. M. Murty's book, "Problems in Analytic Number Theory (2nd edition)". It says: Let $\alpha>0$. Suppose $a_n \ll n^{\...
Q_p's user avatar
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Current status of the research on Universal Logic using Béziau's definition of logical structures as it is

In the book Logica Universalis: Towards a General Theory of Logic Béziau writes (see page 14), My idea was to focus on a logical structure of type $(\mathbb{S}; \vdash)$ where $\vdash$ is a ...
user avatar
3 votes
1 answer
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survey paper on the construction of hyperbolic manifolds

Is there a good survey paper which discusses the common ways of building hyperbolic $n$-manifolds?
student's user avatar
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3 answers
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Remarkable articles about the distribution of prime numbers that were written by contemporary physicists [closed]

I would like to ask about if you know papers containing remarkable achievements that were written by contemporary physicists concerning the distribution of prime numbers (or closely related, maybe the ...
3 votes
1 answer
335 views

Is there a clear criterion or rule about when one can use the heuristic given by Cramér random model for prime numbers?

I don't know if I have misunderstood the information from the section about the heuristic related to Cramér's conjecture and the known facts about Maier's theorem, from the Wikipedia Cramér's ...
user142929's user avatar
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Generalizing CIT-groups to odd case

A CIT-group is a group such that the centralizer of any involution is a 2-subgroup. The structure of these groups is known from the works of Suzuki and others. Here is my question: has the odd case ...
Amin's user avatar
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7 votes
1 answer
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Fractional powers of an operator

What is the large class of operators for which one can define fractional powers? For example, we can consider an operator $A: D(A) \subset X \rightarrow X$, generator of an analytic semigroup on a ...
Migalobe's user avatar
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5 votes
0 answers
111 views

Are affinoid algebras over nontrivially valued fields Jacobson?

It is well-known that for any field $k$ with valuation the Tate algebra $k\{T_1,\dots,T_n\}$ is Jacobson (see Bosch-Güntzer-Remmert for nontrivial valuations; for trivial valuations those are just ...
Wojowu's user avatar
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2 votes
0 answers
381 views

An equivalent statement of the twin prime conjecture

In this paper: Iwaniec and Urroz - Orders of CM elliptic curves modulo $p$ with at most two primes on page 818, the authors claimed in the second paragraph that under some conditions, the statement of ...
Safwane's user avatar
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8 votes
1 answer
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A variant on characteristic $p$ de Rham cohomology

I was thinking about de Rham cohomology in characteristic $p$, and in particular the recent question about Poincare residues, and I came up with the following construction. Let $k$ be a perfect field ...
David E Speyer's user avatar
5 votes
1 answer
348 views

Research work on $ax^n-by^m=1$

I am looking for results on the equation $$ax^n-by^m=1 \tag 1 $$ where $\gcd(m,n)=1$ and $a,b,n,m$ are constants. I found literature for $ax^n-by^n=1$ (R. A. Mollin, D. T. Walker) but couldn't ...
Consider Non-Trivial Cases's user avatar
10 votes
1 answer
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Does every $C_4$-free bipartite graph lies in some finite projective plane?

A projective plane $Π$ is a 3-tuple $(P,L,I)$ where $P$ and $L$ are sets, and $I$ is a relation between $P$ and $L$, such that: For every two elements $p_1$, $p_2\in P$, there exists a unique ...
LeechLattice's user avatar
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6 votes
3 answers
411 views

Universal property of the cocomplete category of models of a limit sketch

Let $\mathscr{S}$ be a limit sketch in a small category $\mathcal{E}$, i.e. just a collection of cones in $\mathcal{E}$. Then its category $\mathbf{Mod}(\mathscr{S})$ of models (i.e. functors $\...
Martin Brandenburg's user avatar
34 votes
1 answer
3k views

Updates to Stanley's 1999 survey of positivity problems in algebraic combinatorics?

[I am a co-moderator of the recently started Open Problems in Algebraic Combinatorics blog and as a result starting doing some searching for existing surveys of open problems in algebraic ...
1 vote
1 answer
87 views

Projection (or idempotent) graph of a $C^*$ algebra(or a ring)

In the literature, are there some research around a directed graph associated to a $C^*$ algebra or a ring $A$ whose vertices are projections or idempotents of $A$ and $e$ is connected to $f$ iff $ef=...
Ali Taghavi's user avatar
5 votes
0 answers
88 views

Progress of the Kazdan-Warner Problem on Higher-genus Surfaces

I would like to understand if there is any further progress of the problem of prescribing Gaussian curvature on (oriented) closed surface $M$ with $\chi(M)<0$ in a conformal class after Kazdan and ...
User's user avatar
  • 402
4 votes
1 answer
670 views

Proof that dynamical systems with bounded Kolmogorov complexity can't emulate all Turing machines

Motivation: During a discussion with neuroscientists the question arose as to whether the human brain may emulate any Turing machine. If we assume that animal brains may be modelled as deterministic ...
Aidan Rocke's user avatar
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1 vote
0 answers
194 views

Karhunen-Loeve expansion of vector valued random processes

This thesis (https://www.semanticscholar.org/paper/Karhunen-Loeve-expansions-and-their-applications-Wang/f173dfb99ec4cbd08e779923770466cf1ef3f138) introduces multivariate KL expansion using a ...
Heisenberg's user avatar
6 votes
2 answers
633 views

Topology/geometry of $O(2n)/U(n)$

I am interested in what is known about the topology (diffeomorphism type) or geometry (is it complex? non-complex? symplectic?) of either the compact space of orthonormal complex structures on $\...
lemon314's user avatar
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21 votes
0 answers
734 views

Is the mapping class group of $\Bbb{CP}^n$ known?

In his paper "Concordance spaces, higher simple homotopy theory, and applications", Hatcher calcuates the smooth, PL, and topological mapping class groups of the $n$-torus $T^n$. This requires an ...
mme's user avatar
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9 votes
1 answer
411 views

Is there a Poincare residue in characteristic $p$?

The Poincare residue I mean is there one here: https://en.wikipedia.org/wiki/Poincar%C3%A9_residue Basically, I would like a nice way to use a meromorphic $n$-form on $\mathbf{P}^n_{\mathbf{F}_p}$ ...
Kim's user avatar
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4 votes
0 answers
345 views

On intrinsic volumes

Let $\Gamma$ be a convex polytope in $\mathbb R^n$. The $k$-th intrinsic volume of $\Gamma$ is the number $$ \text{v}_k(\Gamma)=\sum_{\Delta\in{\mathcal B}(\Gamma,k)}\text{vol}_k(\Delta)\psi_\Gamma(\...
James Silipo's user avatar
14 votes
5 answers
2k views

Reading list for Equivariant Cohomology

I was applying equivaraint cohomology, in particular in the symplectic setting, for some time, but I feel like I am missing some nice books/course notes/articles. Could you advise me some literature, ...
aglearner's user avatar
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5 votes
0 answers
460 views

Open convex hull of a closed set

Let $X$ be a closed set in a Euclidean space of finite dimension and suppose that its convex hull $H$ is open. I can prove that, in this case, $H$ is a Cartesian product of a line with an open convex ...
David Eppstein's user avatar
1 vote
0 answers
220 views

Why is the $\mathbb{Z}_p$-corank of $\operatorname{Sel}_{p^\infty}(E/\mathbb{Q})$ finite?

I'm interested on the Mordell-Weil rank of an elliptic curve over $\mathbb{Q}$. I read that the $\mathbb{Z}_p$-corank of the $p^\infty$-Selmer group $\operatorname{Sel}_{p^\infty}(E)\doteq\...
user avatar
6 votes
1 answer
225 views

Random walks: How many times does the largest component change?

My understanding is that for an unbiased random walk (starting at the origin) on $\mathbb R$ with $N$ steps that the expected number of sign changes is $O(\sqrt N)$. For a biased walk I believe the ...
Daron's user avatar
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11 votes
1 answer
650 views

Are the L-functions of a normalized newform and the corresponding cuspidal representation equal?

Let $f \in S_k(\Gamma_0(N))$ be a normalized newform with Fourier expansion $$f(z) = \sum\limits_{n=1}^{\infty} a_n e^{2\pi i z n}$$ and $a_1 = 1$. Then $f$ is an eigenfunction of all Hecke ...
D_S's user avatar
  • 6,100
0 votes
1 answer
375 views

Rankin-Selberg convolution and product of degrees as of Christmas 2019

Almost 5 years ago (time flies), I asked in Rankin-Selberg convolution and product of degrees whether the Rankin-Selberg convolution of two automorphic representations of respectively $\operatorname{...
Sylvain JULIEN's user avatar
2 votes
0 answers
87 views

Name for a probability density ''symmetrized'' by a permutation group?

Let $p$ be a probability density function over random variable $X$, and $G$ a compact permutation group over the outcomes of $X$. For each $g\in G$, let $p_g$ indicate the probability density ...
Artemy's user avatar
  • 650
2 votes
0 answers
99 views

Closed form expression for this Fourier summation?

Consider the function $f:\mathbb{T}^m\to\mathbb{R}$ $$f(\boldsymbol{x}) = \sum\limits_{{\pmb{\eta}\in\mathbb{Z}^m}}\frac{1}{1+\lambda\|\pmb{\eta}\|_{2k}^{2k} } \cos({2\pi \pmb{\eta}\cdot\pmb{x}})$$ ...
Rajesh D's user avatar
  • 704
11 votes
1 answer
650 views

Correspondences of $\infty$-categories

In Higher topos theory and Higher algebra Lurie defines (see section 2.3.1 of HTT) a correspondence between two $\infty$-categories $C$ and $D$ as being an $\infty$-category $\mathcal{M}$ over $\Delta[...
Simon Henry's user avatar
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3 votes
3 answers
531 views

Did anyone ever introduce an "oscillating unity"?

I wonder whether anyone ever tried to introduce an extension of real numbers by adding an element $\nu$ which would signify the behavior of the function $(-1)^x$ as $x$ goes to infinity? In other ...
Anixx's user avatar
  • 9,306
1 vote
2 answers
154 views

Link btw. exponential and derivatives from an algebraic perspective [closed]

I have been attempting to understand my math education (as a bachelor in electrical engineering) from a more algebraic perspective recently. I would like to understand more about the link between ...
Dacoda Strack's user avatar
4 votes
1 answer
318 views

Examples of particle systems with higher-order collisions

In kinetic theory, one often comes across interacting particle systems with a collisional flavour. I'll currently prefer to think about them as systems of ODEs (or SDEs, Jump Processes, $\ldots$), ...
πr8's user avatar
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7 votes
1 answer
1k views

Quick reference for general Weyl's inequality in number theory

I would like a reference for the result here. Having that $t$ there makes me happy. I would prefer not to have to, in my paper, run through and (not trivially but not too greatly) alter the proof of ...
mathworker21's user avatar
4 votes
1 answer
500 views

A weaker version of the Brocard's Conjecture

Brocard's conjecture states that: If $p_{k}$ and $p_{k+1}$ are consecutive prime numbers greater than $2$, then between $p_{k}²$ and $p_{k+1}²$ there are at least four prime numbers. I know that is ...
Safwane's user avatar
  • 963
1 vote
1 answer
186 views

Almost identical $\sigma$-algebras and measurability

Let $(X,\mathscr X,\mathbb P)$ be a probability space, $(Y,\mathscr Y)$ a measurable space, and $h:X\times Y\to\mathbb R$ a real-valued function measurable with respect to the product $\sigma$-algebra ...
triple_sec's user avatar
2 votes
2 answers
244 views

Approximation of a square with an irrational arithmetic progression

Let $\alpha \in \mathbb{R}\setminus \mathbb{Q}$ be irrational. Does the arithmetic progression $(n\alpha )_{n\in\mathbb{N}}$ becomes arbitrarily close to squares? More precisely, what can be said ...
Amir Sagiv's user avatar
  • 3,544
1 vote
0 answers
76 views

Nomenclature: does this coset space have a name?

in my work I tripped on a specific coset space and before starting thinking about it by myself, I wanted to check the literature. However, I do not know if the object has a name (which makes ...
Riccardo B.'s user avatar
2 votes
0 answers
114 views

English translation of Fouxe-Rabinovitch paper

Is there somewhere an english translation of Fouxe-Rabinovitch's papers "D. I. Fouxe-Rabinovitch, Uber die Automorphismengruppen ¨ der freien Produkte. II, Rec. Math. [Mat. Sbornik] N.S., 1941, ...
1123581321's user avatar
5 votes
1 answer
240 views

Reference for the rectifiablity of the boundary hypersurface of convex open set

The boundary of any convex open set $X$ is $\mathbb R^n$ is a rectifiable hypersurface. To see this, intuitively, simply take a sphere $S_d$ with diameter $d\in(0,+\infty]$ that contains $X$. The ...
High GPA's user avatar
  • 263
4 votes
0 answers
143 views

A Pythagorian inequality characterization of inner-product spaces

Let $(X,\|\cdot\|)$ be a real normed space. For any points $A$ and $B$ in $X$, let $AB:=\|A-B\|$. Suppose that for any points $A$ and $B$ in $X$ and any straight line $\ell\subseteq X$ such that $B\...
Iosif Pinelis's user avatar
3 votes
1 answer
232 views

Regularity and normal trace of "Hdiv" measures

In order to fix the ideas let me consider an open, smooth, bounded domain $\Omega\subset \mathbb R^d$. I am wondering what can be said about a vector-valued measure $v\in \mathcal M^d(\Omega)$ with ...
leo monsaingeon's user avatar
5 votes
0 answers
64 views

Dirichlet-to-Neumann map's estimate for mixed boundary value problems

The study on DtN or NtD maps for Dirichlet or Neumann boundary value problems (or PML for Helmholtz exterior problems) is pretty mature and there are tons of papers on this topic, yet I couldn't find ...
Shuhao Cao's user avatar
4 votes
2 answers
374 views

Bivariate polynomial divisibility test of Spielman

Setup In his thesis (lemma 4.2.18, p. 97-98) Spielman describes a divisibility test for bivariate polynomials $E,P\in k[X,Y]$, where $k$ is a field (of positive characteristic for what I'm interested ...
Olivier Bégassat's user avatar

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