Malik Younsi
|
Registered User
|
|
|
Jun 6 |
comment |
On the existence of a holomorphic logarithm @Margaret Friedland : Thank you for the reference. It seems like a good book, but I didn't find what I'm looking for. |
|
Jun 5 |
comment |
On the existence of a holomorphic logarithm Yes, this is the proof I had in mind, thank you. However, I was wondering : do you have any idea where I could look to find a reference for this result? It is quite natural, so I am pretty sure it appears somewhere in the literature, but I couldn't find anything. |
|
May 31 |
comment |
On the existence of a holomorphic logarithm @Andreas Blass : Yes indeed, but I meant under which conditions on $\Omega$ and $f$ does the above holds. In particular, I think it is true if $f$ does not reverse orientation of curves inside $\Omega$. |
|
May 31 |
comment |
On the existence of a holomorphic logarithm @Etienne Matheron : In general, $f(z)=(z-a)^2$ is not necessarily one-to-one on $\Omega$. You probably mean that $f(z)=1/(z-a)$ is a counterexample. |
|
May 31 |
comment |
Is the homeomorphism class of a connected open set of C determined by its fundamental group? @EtienneMatheron : The unit disk is homeomorphic to $\mathbb{C}$, for example via $f(z)=z/(1-|z|^2)$. These sets are not conformally equivalent, though. |
|
May 31 |
revised |
On the existence of a holomorphic logarithm deleted 12 characters in body |
|
May 31 |
revised |
On the existence of a holomorphic logarithm added 170 characters in body |
|
May 31 |
revised |
On the existence of a holomorphic logarithm deleted 249 characters in body |
|
May 31 |
comment |
On the existence of a holomorphic logarithm We have $e^g=-1/z^2$, and thus $e^{-g}=-z^2$. How do you obtain $e^{-2g}=z$? But I believe this gives a counter-example because -z^2 does not have a holomorphic logarithm on $\mathbb{C} \setminus \{0\}$. Clearly I overlooked something this morning... Thank you |
|
May 31 |
revised |
On the existence of a holomorphic logarithm added 236 characters in body |
|
May 31 |
asked | On the existence of a holomorphic logarithm |
|
May 27 |
comment |
Riemann mapping Welcome to MO, Maxime Fortier Bourque! |
|
Apr 3 |
answered | functions of one complex variable: geometric theory |
|
Mar 30 |
awarded | ● Popular Question |
|
Mar 12 |
comment |
On the set of zero radial limits of bounded analytic functions @Giuseppe : Thank you! |
|
Mar 12 |
comment |
On the set of zero radial limits of bounded analytic functions Thank you very much for the interesting references, I will take a look at them. |
|
Mar 10 |
comment |
On the set of zero radial limits of bounded analytic functions I'm having some problem with LaTex in the definition of $Z_f$... Does someone know how to fix that? |
|
Mar 10 |
asked | On the set of zero radial limits of bounded analytic functions |
|
Feb 20 |
comment |
Undecidability and holomorphic functions (Reference request) The proof is very elegant, and it appears in "Proof from the Book" by Aigner and Ziegler. |
|
Feb 8 |
awarded | ● Fanatic |
|
Jan 29 |
awarded | ● Enlightened |
|
Jan 29 |
awarded | ● Nice Answer |
|
Jan 28 |
comment |
When does continuity imply holomorphy? @EmilJeřábek : I didn't know about the removability criterion for the Hölder functions. This is very interesting. |
|
Jan 28 |
accepted | When does continuity imply holomorphy? |
|
Jan 28 |
revised |
When does continuity imply holomorphy? added 9 characters in body |
|
Jan 28 |
answered | When does continuity imply holomorphy? |
|
Jan 28 |
awarded | ● Popular Question |
|
Jan 26 |
comment |
On the Universality of the Riemann zeta-function @MarcPalm : Yes, indeed, I see now why we need $\log$. But still, it is a good idea to work with joint universality. Thanks, +1 ! |
|
Jan 25 |
comment |
On the Universality of the Riemann zeta-function I mean, the result I'm looking for should contain Voronin's Universality Theorem as a particular case (the case when the complement of $K$ is connected). |
|
Jan 25 |
comment |
On the Universality of the Riemann zeta-function Oh I see, indeed I misread $K_0$ for $K$, sorry about that! But I don't understand why you work with $\log$..? |
|
Jan 24 |
comment |
On the Universality of the Riemann zeta-function See my new edit. I hope it clarifies what I'm looking for here. |
|
Jan 24 |
revised |
On the Universality of the Riemann zeta-function added 820 characters in body; added 7 characters in body |
|
Jan 24 |
comment |
On the Universality of the Riemann zeta-function This joint universality result is interesting, but what I'm looking for is really a result for compact sets with disconnected complements. Also, just to clarify : I don't want to remove the non-vanishing assumption. I'm fine with it! |
|
Jan 22 |
awarded | ● Nice Question |
|
Jan 22 |
revised |
On the Universality of the Riemann zeta-function deleted 401 characters in body; added 11 characters in body |
|
Jan 21 |
revised |
On the Universality of the Riemann zeta-function added 491 characters in body; added 2 characters in body; added 11 characters in body |
|
Jan 21 |
comment |
On the Universality of the Riemann zeta-function @MarcPalm : There is definitely a confusion here. I am talking about Mergelyan's theorem on uniform approximation by rational functions. Of course, uniform approximation by polynomials is only possible in the "connected complement" case! I'll edit the question for more clarity. |
|
Jan 21 |
comment |
On the Universality of the Riemann zeta-function @MarcPalm : See my comment to the question... There is a confusion here. |
|
Jan 21 |
revised |
On the Universality of the Riemann zeta-function added 135 characters in body |
|
Jan 21 |
revised |
On the Universality of the Riemann zeta-function edited body |
|
Jan 21 |
revised |
On the Universality of the Riemann zeta-function deleted 8 characters in body |
|
Jan 21 |
comment |
On the Universality of the Riemann zeta-function @JohannesEbert : Do you think the question is clear now? |
|
Jan 21 |
revised |
On the Universality of the Riemann zeta-function added 126 characters in body; added 11 characters in body |
|
Jan 21 |
comment |
On the Universality of the Riemann zeta-function Yes, of course, the theorem, as stated, does not hold if you remove the hypothesis that the complement of $K$ is connected. I'm asking if there exists a (different) universality-like result that would work for compact sets with disconnected complements. Sorry if that wasn't clear, I'll edit the question... |
|
Jan 21 |
revised |
On the Universality of the Riemann zeta-function deleted 36 characters in body |
|
Jan 21 |
asked | On the Universality of the Riemann zeta-function |
|
Jan 2 |
awarded | ● Necromancer |
|
Dec 30 |
revised |
A question about the limit of a sequence of pointwise convergent analytic funtions added 237 characters in body |
|
Dec 30 |
answered | A question about the limit of a sequence of pointwise convergent analytic funtions |
