8 votes

On Cramér's theorem about roots of Zeta function

Q1: There is a functional relation for $V(z)$, but no "explicit expression" I know of. Q2: Cramér's paper is from 1919, a modern and more extensive treatment is in On Cramér's theorem for ...
user avatar
6 votes

Free algebras from model theory perspective

Here are some papers. (1) Baldwin, J. T.; Shelah, S. The structure of saturated free algebras. Algebra Universalis 17 (1983), no. 2, 191-199. From the Math Review (written by Steve Comer): The authors ...
user avatar
4 votes

Can you perturb an inscribed polytope so all its edges grow?

OK, let me address the case of a simplex. In fact, it follows from the `dual Kneser--Poulsen'conjecture, as stated, e.g., in this nice paper. A good thing is that the simplex has only $n+1$ vertices, ...
user avatar
4 votes

Reference request: Left $R/k$-modules

This is a very basic question. See e.g. Section 1.1 of the book: R.S. Pierce: Associative algebras, Graduate Texts in Mathematics, 88. Springer-Verlag, 1982.
user avatar
4 votes

Reference for an easy lemma on homeomorphisms of connected manifolds

In [Ancel and Bellamy, On homogeneous locally conical spaces, Fund. Math. 241 (2018), no. 1, 1–15] it is shown that every homogeneous locally conical connected separable metric space that is not a $1$-...
user avatar
4 votes

Reference request : table of quantum Clebsch-Gordan coefficient

For rank-two quantum groups the Clebsch-Gordan coefficients are tabulated in arXiv:1004.5456 by Ardonne and Slingerland. This also includes mathematica notebooks to perform these and similar ...
user avatar
3 votes
Accepted

Is Schwartz space $\mathbb R^n$ contained in every fractional Sobolev space on $\mathbb R^n$?

One way to approach such questions is to start with an abstract situation (Hilbert scales). If $T$ is an unbounded s.a. operator with $T>1$ on a separable Hilbert space (in your case, the ...
user avatar
3 votes
Accepted

Strong form of $\mathtt{PSP}$ for $K_\sigma$ sets

Here's a counterexample. Let $X$ be the set of bounded sequences, and let $A$ be the set of sequences which have only finitely many nonzero terms and achieve a strict maximum at the last nonzero term. ...
user avatar
2 votes
Accepted

Uniform boundedness Schrödinger operator eigenfunctions with Dirichlet conditions

Yes, this follows because asymptotically, as $|z|\to\infty$, the solutions of $-y''+Vy=zy$ look like those of the free equation $V\equiv 0$, and the eigenfunctions of $-y''=zy$, $\phi_n=(2/(L\pi ) )^{...
user avatar
1 vote

Reference for an easy lemma on homeomorphisms of connected manifolds

I suppose we induct on $n$ (the number of points) and appeal to some version of "Guggenheim's theorem". I started by looking in "Introduction to piecewise linear topology" by ...
user avatar
  • 18.5k
1 vote
Accepted

References and updates on a $L^p$ Factorization theorem by Maurey

I mentioned in another of your posts the book of Diestel, Jarchow,and Tonge. Chapter 7 in the book of Albiac and Kalton, "Topics in Banach space theory", contains a nice exposition of Maurey'...
user avatar
  • 29.5k

Only top scored, non community-wiki answers of a minimum length are eligible