2,371 reputation
3924
bio website www-irma.u-strasbg.fr/…
location Strasbourg
age 37
visits member for 2 years, 10 months
seen 14 mins ago
I'm working on complex dynamical systems, more specifically on the local/global aspect of singular holomorphic foliations in the complex plane

1d
revised For what real $t$ is $\{n^t : n \geq 1\}$ linearly independent over $\mathbb{Q}$?
LaTeX
Apr
24
comment Multivariable function analysis
If you differentiate with respect to $k$ the relation $f(\alpha(k))=0$ and require $\alpha'(k)=0$, you obtain $k=\frac{\ln\frac{\ln\alpha(k)}{\ln2}+n\ln\alpha(k)}{\ln\alpha(k)-\ln 2}$. Don't know if that helps, though, but it may if you have some kind of control on $\alpha$ as the largest root.
Apr
19
comment If $f$ is separately holomorphic on $\Omega$ then $f\in\mathcal{C}^0(\bar\Omega)\Leftrightarrow f\in L^1(\Omega)$
@ChristianRemling: I agree with you, yet maybe you could consider making this a short answer just for the sake of closing the question...
Apr
19
reviewed Approve Eigenvalues of Matrix Sums
Apr
19
revised Zero divisors and boundary elements of $A^{-1}$
added 7 characters in body; edited title
Apr
19
reviewed Approve Zero divisors and boundary elements of $A^{-1}$
Apr
15
reviewed Approve How does a level set look like when the minimum point of a function degenerate?
Apr
10
reviewed Approve What's the “best” proof of quadratic reciprocity?
Apr
2
reviewed Approve What is the best graph editor to use in your articles?
Mar
18
reviewed Approve hyperbolic metrics
Mar
17
revised Are all rational exactly solvable differential equations known?
added 286 characters in body
Mar
17
comment Automorphisms of $\mathbb{C}$ and meromorphic functions
Ok, thank you for the precision.
Mar
17
comment Automorphisms of $\mathbb{C}$ and meromorphic functions
Maybe there is something I don't understand, but the $\sin$ function both defines $\mathbb Z=\{z : \sin (z)=0\}$ and $\mathbb R=\{z : \sin (z)=\overline{\sin (z)}\}$.
Mar
17
comment Are all rational exactly solvable differential equations known?
Nothing, I understood what you said. I just included the second piece because if you want to achieve effective, concrete algorithms then the issue pops up (although it also does in the first piece). But I understood your concern was at a higher-level of calculability. That being said, I still somehow believe that a lot of undecidability lies down there ;)
Mar
17
answered Are all rational exactly solvable differential equations known?
Mar
17
comment Are all rational exactly solvable differential equations known?
You must specify what you mean by both «decide» (and therefore what conditions you put on the coefficients of the differential equation, e.g. belonging to a field where you can decide the equality to $0$ with a halting turing machine) and «exactly solvable» (I assume you mean integrability by quadrature in the sense of Liouville). Even being granted the two defaulted meanings above, I fear that there are no known answer to your question, although it is believed by some that the Poincaré question (solvable by rational first-integral) is undecidable. The key-word is differential Galois theory.
Mar
17
reviewed Approve Is it true that for each bounded continuous function we can find a set of analytic functions to uniformly converge it?
Mar
16
comment the impossibility of exactly computing eigenvalues
It is sufficient to take $p$ with non-solvable Galois group. Take your favorite non-solvable real quintic polynomial. Now the diagonal matrix with diagonal entries the real roots of this polynomial is hermitian. This question is not research level in its present form. E.g. you should precise what you mean by "explicit formula" and on which field you work, to avoid stupid trivial answers as the one I just gave.
Mar
15
reviewed Approve Motivation for concepts in Algebraic Geometry
Mar
11
reviewed Approve More recently published comprehensive reference on inequalities in the spirit of Hardy-Littlewood-Pólya