Questions tagged [reference-request]

Question 1

I'm working in the category of schemes over $\mathbb C$ or algebraic varieties over the same. Here by line I mean any curve isomorphic to $\mathbb P^1$, of any degree; i.e. the twisted cubic is a line....

Question 2

Vieta's formulas are well known. $$\sum _{1\leq i_{1}<i_{2}<\cdots <i_{k}\leq n}\left(\prod _{j=1}^{k}r_{i_{j}}\right)=(-1)^{k}{\frac {a_{n-k}}{a_{n}}}$$ For example, the sum of the roots of ...

Question 3

Question. Is there a simpler way to prove $$B_{2k+1}(1/4) = \frac{-(2k+1) E_{2k}}{4^{2k+1}}$$ where $B_n(x)$ is the $n$-th Bernoulli polynomial and $E_n$ is the $n$-th Euler number? I have verified ...

Question 4

I am looking for references (textbooks or articles) where it is shown that the Banach space $\ell^1$ has the Kadec–Klee property, i.e. that the weak topology and the norm topology coincide on the unit ...

Question 5

What is a reference of the fact that on connected, positively curved, compact Riemannian manifolds (such as the sphere) $M$ with dimension $d$, the following inequality $$\|f\|_{L^\infty(M)} \lesssim \...

Question 6

I'm currently taking a number theory course, specifically a representation of reductive p-adic groups. To work through examples, could someone recommend me books or lecture notes that explain ...

Question 7

Given a finitely generated smooth $k$-algebra $A$ (the case where $A=k[X_1,...,X_n]$, or a localization of this, is the one I am actually interested in) and a finite extension $B$ of $A$, I am ...

Question 8

I have been looking at sums with binomial coefficients in their denominator. These are extensions of Apery's series, which he used in his proof of the irrationality of $\zeta(3)$. This weekend I ...

Question 9

Suppose that $E_0, E_1 \rightarrow M$ are two $k$-dimensional vector bundles over a manifold $M$ classified by maps $\phi_0, \phi_1: M \rightarrow BGL(k)$. If $\phi_0, \phi_1$ are homotopic, then $E_0,...

Question 10

This is a reference request; is this particular generalization of the $3\cdot n+1$ problem discussed in literature? What is known about it? Do any specific choices of $m$, $a_i$ lead to nontrivial yet ...

Question 11

Let $R := \mathbb C[x_1,\dots,x_d]/J$ be an affine domain which is the coordinate ring of the affine variety $X = V(J) \subseteq \mathbb C^d$. Let $M \in R^{m\times(n+1)}$ be a matrix with entries ...

Question 12

I'm interested in the following problem in statistical characteristics of graph embedding, and it seems to fall between traditional graph theory and Graph neural networks. I looked up: William L. ...

Question 13

I am working on a project that combines ingredients from geometric group theory and spectral graph theory, and I would appreciate references (papers, authors, or survey articles) that study anything ...

Question 14

Let $\Omega \subset \mathbb{R}^n$ a bounded domain, $f:\mathbb{R} \to \mathbb{R}$ of class $C^1$ such that $f(0)=0$. Let $u \in L^{\infty}(\Omega) \cap W_0^{1,p}(\Omega)$ for some $1 \leq p <+\...

Question 15

Let $(M, \tilde{g})$ be a Riemannian manifold and let $g:=e^{2u}\tilde{g}$ be a conformal change. I'm trying to find a resource (ideally a book, or a paper where it's mentioned or derived) for the ...

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Questions tagged [reference-request]

Are there any lines on an Abelian surface?

Creative Alternatives to Vieta's formulas/Newton's identities

Prove $B_{2k+1}(1/4) = \frac{-(2k+1) E_{2k}}{4^{2k+1}}$

Reference request: Kadec-Klee property for $\ell^1$

Reference request on Sobolev inequality on compact manifolds.

Could someone recommend me some references for algebraic groups? [closed]

Literature on Differential Forms of finite extensions of smooth $k$-algebras

Reference request for some sums

Vector bundles with equivalent sphere bundles

Reference request: a particular generalization of the Collatz problem

Ideal of maximal minors is radical when rank never drops by more than 1 [Reference request]

Good Textbook or Relevant Literatures for Learning Graph Embedding

Looking for authors/papers in GGT involving piecewise isometries, free group actions, and twisted Ihara zeta functions

Composition in Sobolev Spaces [duplicate]

Reference for the formula for conformal change of sectional curvature

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