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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
Mathoverflow.net news digest
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0 days
Let $M$ denote the set of Borel measures on the complex plane with compact support and where $\mu(\mathbb{C})<\infty$. We endow $M$ with the weak$^*$-topology which is the smallest topology such that whenever $f:\mathbb{C}\rightarrow\mathbb{R}$ is...
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0 days
On the sum of Kloosterman sum of degree 4
I have a puzzle which needs some helps from the experts here.Let the Kloosterman sum of degree 4 be as follows:$$S_4(1,n;c)=\hskip 0.5em \sideset{_{}^{}}{^{\ast}_{}}\sum\limits _{x,y,z \bmod c} e \left (\frac{nx+y+z+\overline{xyz}}{c}\right).$$
My question is: could we expect a bound like$$\sum_{c\sim C} K_4(1,n;c)\ll C^{2-\varepsilon}\,\,?$$Note that the individual bound for $K_4(1,n;c)$ is $\ll c^{3/2+\varepsilon}$. As far as I know, this type of sum was considered for degree two case, i... -
13 years
Connected sum of topological manifolds
A definition of the connected sum of two $n$-manifolds $M$ and $M'$ begins by considering two $n$-balls $B$ in $M$, $B'$ in $M'$, and glueing the varieties $M\setminus \mathring B$ and $M'\setminus \mathring B'$ along their boundary (an $(n-1)$-sphere...
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0 days
Connections between the Hamilton-Jacobi equation and the Ricci flow equation
The Hamilton-Jacobi equation of symplectic geometry states:$$\frac{\partial S}{\partial t} + H\!\left(q,\frac{\partial S}{\partial q},t\right)=0\tag1,$$
it is a nonlinear PDE for the generating function $S(q,t)$ (the phase of the wavefunction if you will) and the graph of the gradient of $S$ is the Lagrangian submanifold in phase space:...
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