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Q&A for professional mathematicians
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
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Hottest Questions Today - MathOverflow
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Mathoverflow.net news digest
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0 days
Resolving a coherent sheaf via pullbacks
Let $X$ be some projective variety, and $\mathcal{F}$ be some coherent sheaf on $X$ with nonfree locus of high codimension. Is it possible to construct some finite map $f:Y\to X$ such that $f^*\mathcal{F}$ (modulo torsion) is actually a vector bundle...
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4 years
Putnam 2020 inequality for complex numbers in the unit circle
The following simple-looking inequality for complex numbers in the unit disk generalizes Problem B5 on the Putnam contest 2020:
Theorem 1. Let $z_1, z_2, \ldots, z_n$ be $n$ complex numbers such that $\left|z_i\right| \leq 1$ for each $i \in \left\{1,2,\ldots,n\right\}$. Prove that\begin{align}\left| z_{1} + z_{2} + \cdots + z_n - n \right|\geq\left| z_{1} z_{2} \cdots z_n -... -
11 years
Are all complex zeros of $\frac{\Gamma(s)}{z}Li_s(z) \, \pm \, \frac{\Gamma(1-s)...
Numerical evidence suggests that all complex zeros residing in the critical strip $0 < \Re(s) < 1$ of:
$$\frac{\Gamma(s)}{z}Li_s(z) \, \pm \, \frac{\Gamma(1-s)}{z}Li_{1-s}(z)$$
are on the critical line $\Re(s)=\frac12$ for all $z \lt 1$ (with both individual terms $\ne 0$, except when $z=-1$).... -
0 days
Using a totally ordered monoid to assign a measure to subsets of natural numbers
Greetings to everyone at MOF. I am a very beginning student of mathematics, and one of the reasons I study mathematics on my own is that I could not find an answer to a simple question: "How can one perfectly compare two subsets of natural numbers?"...
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