0
votes
0answers
10 views
Residue fields of attached to coefficients of modular forms
Let $f = \sum_n a_n q^n$ be a cuspidal newform of some weight and level. Here I want to view the $a_n$ of $p$-adic numbers (by embedding $\overline{{\bf Q}}_p$ in ${\bf C}$ in so …
6
votes
1answer
32 views
Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?
Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers? Which of their properties and relations (e.g. usual trig ident …
6
votes
0answers
31 views
A double grading of catalan numbers
This is something I found in trying to work on Vince Vatter's excellent question. I have no solution, but a much more precise conjecture.
Recall that a rooted planar tree is a roo …
0
votes
0answers
15 views
How can this fail if my pairing is nondegenerate?
I have two infinite-dimensional (Frechet) linear spaces $X$ and $Y$ over $\mathbb R$, and a nondegenerate pairing $\langle\cdot,\cdot\rangle:X\times Y\to \mathbb R$. Neither $X$ no …
1
vote
0answers
19 views
Existence of particular embeddings in euclidean spaces for non compact manifolds
Let $M$ be a $n$-dimensional smooth connected not compact manifold s.t. groups (singular cohomology)
$H^{k}(M,\mathbb{Z})$ are finitely generated for $k\geq 0$. Can we find a suff …
1
vote
4answers
243 views
Where is the belly button of the Universe?
It's fine and nice and wonderful when a part of learning mathematics is chaotic, ad hoc, spontaneous, social, ...
However it would be perhaps of fundamental value to know a very c …
0
votes
0answers
30 views
What is the inverse of this kind of integral transform?
Let $$\hat{f}(\lambda):= \int_0^{+\infty}K(x,\lambda)\ f(x)\ dx, \text{where } K(x,\lambda)=\sqrt{\frac{2}{\pi}}\frac{\lambda \cos(\lambda x)+h\sin(\lambda x)}{\lambda^2+h^2}$$
be …
1
vote
1answer
27 views
Closure of one relation w.r.t other
I have two relations R and R' satisfying following property -
R(a,b) & R'(a,a') & R(a',b') => R(a,b')
Pictorially, it looks like this -
a --(R)-> b
| \
(R') \ (* n …
0
votes
0answers
13 views
Why this synchronization error dynamic for Krasovskii-Lyapunov?
I am attempting to work through "Shahverdiev, Sivaprakasam, and Shore (2002) Lag synchronization in time-delayed systems", but I'm missing something basic up front.
The problem is …
3
votes
0answers
113 views
Why did Bourbaki not use universal algebra?
I have seen a discussion about Bourbaki’s usage of categories before. So let me ask a different question: why did he not use universal algebra?
Well, universal algebra is not much …
1
vote
0answers
14 views
How many trees can be constructed from k vertices using an LCA operator?
Consider the class of rooted trees and suppose I have at my disposal a lowest common ancestor (LCA) operator given by
$$
\textrm{lca}(u,v) = \text{the lowest common ancestor of $u$ …
0
votes
1answer
18 views
Extension of equivalent norms
Let $(X,||\cdot||_1)$ be a normed space and $Y$ a linear subspace of $X$. Let $||\cdot||_2$ be a norm on $X$ which is equivalent to $||\cdot||_1$ on $Y$. Does there exist a norm on …
1
vote
0answers
81 views
Why does Grothendieck’s period conjecture imply Hodge’s conjecture ?
Hello to all of you :
I would like to know if it is true that the Grothendieck period conjecture implies the Hodge conjecture in the case of non-singular complex algebraic varietie …
0
votes
0answers
37 views
Can Hartogs' extension theorem be used to prove there’s no naked singularity?
Maybe for the first time my question doesn't deal with number theory. Tonight a friend of mine told me about Hartogs' extension theorem and said his work in analytic microlocal ana …
0
votes
3answers
58 views
Does this ODE system have solution?
Let $A(t)$ and $B(t)$ be matrices with each element in $L^\infty(0,T).$ Let $A(t)$ have an inverse. I know nothing else about this inverse.
Let $c(t)$ be a vector in $L^2(0,T).$ …
