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 Dec 18 comment positive integer composite numbers $n$ such that $n$ divides $3 ^ {n-1} - 2 ^{n-1}$ [I don't know if a comment is a right way to ask this, if not I apologize] This exercise actually comes from a Telematic Selection Test for high school students for Italian Mathematical Olympiads which will end on December 30th ... is it possible to put the topic on hold until that date? Dec 4 awarded Yearling May 16 comment $f$ convex: exists linear map $g$ s.t. $f\geq g$? what are $x$ an $y$? Or better how are they quantified? Exists $x$? For every $y$? Apr 16 answered Functions belonging to $L^p(\mathbb{R}^n ; \mathbb{R}^m)$ if and only of their norm belongs to $L^p(\mathbb{R}^n)$ Apr 15 revised Inequality involving trace and operator norm added 115 characters in body Apr 15 comment Inequality involving trace and operator norm I don't understand what happened, but I never wrote the first 4 lines (which are false: eigenvalues of W are all real and positive, as the characteristic polynomial is $(t-1)^2$ no matter what $a$ is... Apr 13 comment Residue theorem Yes, that is what i was trying to point out in my comment! Sorry for my elapsed time of response, but this allowed you to figure it out by yourself! Apr 11 comment Residue theorem why do you say that $g(z)=e^{itz}e^{-Im(z)}/(z+i)$ is holomorphic? Apr 8 answered Chain rule in several complex variables: Wirtinger derivatives Apr 8 answered Does in this case exist necessarely an eigenvalue equal to $0$? Apr 7 comment Does in this case exist necessarely an eigenvalue equal to $0$? The Levi form is defined as the complex Hessian of a defining function restricted to the complex tangent hyperplane, i.e. to a space of dim $n-1$. So, if you start with a (Levi)convex hypersurface and you write it locally as $y_1=Q+hot$ around the origin, the Levi form in the origin will be restricted to the hyperplane $z_1=0$ (the vanishing direction you were complaining about) Apr 6 revised Is an hypersurface uniquely determined by an equation? edited tags Apr 6 comment Is an hypersurface uniquely determined by an equation? Well, $r^3=0$ defines the same hypersurface locally around $z_0$. As it does $r(z)(\|z\|^2+1)=0$... Apr 2 answered integrating by parts on a manifold Mar 21 comment Is $\sum_{n=1}^\infty \sin\left(\frac{n\pi}{4}\right)$ convergent? It is the first result that is proved to you in any calculus course just after defining what is a series of real numbers. If $s_n$ is the sequence of partial sums ($s_n=a_0+..+a_n$), the sum converges to $S$ if and only if $s_n\to S$, hence $a_n=s_n-s_{n-1}\to (S-S)=0$. Mar 21 revised How to evaluate $\frac{1}{2\pi i}\int_C \frac{f(z) dz}{(z-z_1)^{m_1}(z-z_2)^{m_2}}$ and the other related contour? added 4 characters in body Mar 20 answered How to evaluate $\frac{1}{2\pi i}\int_C \frac{f(z) dz}{(z-z_1)^{m_1}(z-z_2)^{m_2}}$ and the other related contour? Mar 19 comment Unique continuous complex log of a function nowhere zero Probably in this book springer.com/birkhauser/mathematics/book/978-0-8176-4164-1 there is enough stuff for your needs. Mar 16 comment Unique continuous complex log of a function nowhere zero You don't select any branch. You just go on along the path defining the logarithm by analytic continuation... Mar 15 comment Relation between being holomorphic in $\Delta\times\Delta$ and in every relatively compact polydisk. If I guess correctly, this is a step in the proof of Hartogs theorem about separate analyticity. There you take a domain $U$ and prove that $f$ is holomorphic on every relatively compact polydisc. If this is the situation, you have that the hypotheses hold in a neighbourhood of the polydisc, so that you can enlarge the strip a bit.