2
votes
0answers
10 views
Article about intersection in manifolds
Hello, can someone please help me find the following article:
M. Glezerman, and L. Pontryagin, Intersection in Manifolds. Translation No 50, New York: american mathematical societ …
3
votes
0answers
12 views
Amalgamation of two ccc algebras may collapse the continuum
The claim that appears in the title of this question is mentioned in the paper "On Shelah's amalgamation" by Judah and Roslanowski. I'd really like to see a proof of this fact, but …
0
votes
0answers
7 views
Norm estimation of an area integral
I am solving a certain kind of integral equations using iteration and Volterra series. Now I get a formal solution and in order to prove convergence I need to estimate the $L^1$ an …
5
votes
0answers
94 views
Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?
I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to complex lo …
1
vote
1answer
43 views
Given an even integer N, what is the minimum set of primes such that any even number x <= N can be expressed as the sum of two primes from the set?
Given an even integer N, what is the minimum set of primes such that any even number $x \leq N$ can be expressed as the sum of two primes in the set?
Goldbach's conjecture said Ev …
0
votes
1answer
40 views
Any closed form for series like $F(x)=\Sigma_{i=p}^{\infty}x^p$,p is prime$?
Any closed form for series like $$F(x)=\Sigma_{i=p}^{\infty}x^p,\text{p is prime}$$ or $$F(x)=\Sigma_{i=0}^{\infty}x^{i!}$$?
More generally,we can obtain a power series from decim …
4
votes
1answer
237 views
Why has Bourbaki ignored the theory of categories?
They had plenty of time to adopt the theory of categories. They had Eilenberg, then Cartan, then Grothendieck. Did they feel that they have established their approach already, that …
0
votes
0answers
6 views
Asymptotic bounds on $\pi^{-1}(x)$ (inverse prime counting function)
What are the current best asymptotic bounds on $\pi^{-1}(x)$, where $\pi(x)$ denotes the prime counting function (number of primes at most $x$)?
In other words, I am curious about …
0
votes
1answer
46 views
Complete D.V.R’s That have different characteristic than the residue field
I'm working through Local Fields by Serre and am stumped by something that he thinks should be obvious.
Let $A$ Be a complete D.V.R with uniformizer $\pi$ and $\overline{K}$ be i …
19
votes
3answers
297 views
A family of words counted by the Catalan numbers
In recent work with Michael Albert and Nik Ruškuc, a family of words has arisen which is counted by the Catalan numbers. I've looked at Richard Stanley's Catalan exercises in EC2 a …
0
votes
1answer
55 views
Canonical Modules
Is there a decent way to describe the canonical module of the ring $\frac{\mathbb{C}[x,y,z]}{x^2-yz}$? I am not necessarily looking for an explicit description of the canonical mod …
1
vote
1answer
50 views
Decomposition into irreducibles of symmetric powers of irreps.
Suppose I have an irreducible representation of a simple Lie algebra, say $\mathfrak{sl}(n)$ or $\mathfrak{so}(n)$ i.e., $A$ and $D$ type. Given such a representation, $\Gamma_\lam …
2
votes
2answers
179 views
Field generated by the Fourier coefficients of a modular form
Let $f = \sum_n a_n q^n$ be a cuspidal newform of weight $k$ on $\Gamma_0(N)$ for some $N$. Let $K_f$ be the number field generated by the $a_q$ as $q$ runs over all primes.
My q …
0
votes
0answers
20 views
Proof that a finitely generated projective module over a Von Neumann Regular ring is free
I'm searching for a proof that a finitely generated projective module over a Von Neumann Regular ring is free. I know that this result is true, because a friend of mine have proved …
2
votes
1answer
59 views
Even more generalized Catalan numbers
What is the number of ways to parenthesize $n$ elements using applications of operators of arbitrary arities larger than or equal to $2$? For example, for $n=3$, there are $3$ ways …
