1
vote
3answers
224 views
Help with this Diophantine equation
Note: This question was posted in error, and should be closed as no longer relevant. The correct question is posted at http://mathoverflow.net/questions/131353/help-with-this-sys …
2
votes
0answers
25 views
Duality between K-theory and K-homology in the non-compact, spin$^c$ case
Let $M$ be a compact spin$^c$ manifold, so that it has a fundamental class $[M] \in K_n(M)$. It is well-known that the cap product with $[M]$ induces Poincare duality isomorphisms …
2
votes
2answers
115 views
Help with this system of Diophantine equations
A couple hours ago, I'd posted a Diophantine equation question, but realized that I'd committed a rather preposterous blunder deriving it.
This is the actual question which I'm tr …
2
votes
1answer
274 views
Probability $k$ bins are non-empty.
The following problem arises in the analysis of Bloom filters.
Consider $m$ bins and $N=nk$ balls placed uniformly at random into the bins. A query chooses $k$ bins uniformly at …
0
votes
2answers
74 views
Why every complex of injectives is homotopically injective (provided that, the injective dimension is finite)?
Let $\scr A$ be an abelian category with exact products and a cogenerator (e.g. $\scr A$ is a category of modules). Let ${\mathbf K}(\scr A)$ be the homotopy category of cochain c …
1
vote
0answers
30 views
Non-crystallographic cluster algebras
Background
Fomin and Zelevinsky have introduced cluster algebras in an influential article. To define a cluster algebra, Fomin and Zelevinsky have defined a mutation of seeds. Her …
0
votes
0answers
42 views
Circle segment of exact length [closed]
I need to find:
a spherical line
that passes through the points 0,0 and 8,8
and the distance of the line between those two points must be exactly 12
I imagine the answer will b …
-1
votes
0answers
53 views
What is the perimeter of the figure shown on the coordinate plane? [closed]
What is the perimeter of the figure shown on the coordinate plane?
Picture
http://imgur.com/r4CNd4y
1
vote
1answer
90 views
fundamental class is the sum of simplices of triangulation of the manifold?
M is an n-dimensional closed orientable manifold. I find in a book "Intuitively,the fundamental class can be thought of as the sum of the (top-dimension) simplices of a suitable tr …
1
vote
1answer
62 views
Non-(stable)-triviality of the tautological bundles
This is a question I asked at Math.SE but got no answers: http://math.stackexchange.com/q/396217/7110/
The tautological vector bundle $\gamma_k(\mathbb{K}^N)$ over the Grassmann m …
2
votes
1answer
71 views
Field of definition of canonical morphism between (congruence) modular curves
Let $\Gamma\subseteq \Gamma'\subset SL_2(\mathbb Z)$ be congruence subgroups, and
$X(\Gamma)$, $X(\Gamma')$ be the associated smooth projective modular curves over $\mathbb C$. Th …
40
votes
2answers
4k views
Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture
Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville:
“The big experts in the field had
already tried to make this approach
w …
0
votes
0answers
20 views
How to simplify this Kampé de Fériet function?
I was dealing with a convolution type integral
$$
\int^z_0 t^m {}_0F_1(;1;-t) \: {}_2F_3\Big( 1,1;2,m,m+1 ; -a t\Big) \:\mathrm{d}t
$$
By applying one of the identities in Exton's …
1
vote
1answer
140 views
a question of local field
Let $K$ be a local field with mix char, $k$ residue field. We have an exact sequence
$0 \longrightarrow I \longrightarrow G_{K} \longrightarrow G_{k} \longrightarrow 0$
Then we o …
3
votes
2answers
106 views
Quotients in Sums of Rings
Suppose we are given a commutative ring R with unit-element. Now we have a composition of R as the direct product of two rings $R\cong R_1\times R_2$. It is now straight forward, …
