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Oct
18
answered Functoriality of fundamental group
Oct
18
comment extension of holomorphic functions on complex manifold
A holomorphic function on a compact complex manifold is constant, so the only functions on $M\setminus D$ which can extend are the constant ones...
Oct
17
comment Finding all natural $n$ such that $2^n+2^{2n} +2^{3n}$ has only $2$ prime factors.
@Leo163: yes, sorry, you edited the post after I had written the comment …
Oct
17
comment Finding all natural $n$ such that $2^n+2^{2n} +2^{3n}$ has only $2$ prime factors.
for $n=3$ you have $2^3+2^6=72=73-1$, so a solution with $p=73$, $a=1$, but $p\neq 2^n+1$...
Oct
17
answered Finding all natural $n$ such that $2^n+2^{2n} +2^{3n}$ has only $2$ prime factors.
Oct
17
answered Analytic function on a circumference
Oct
15
comment classification of boundary values of one complex variable holomorphic functions
So if $f(z)=\sum_n a_nz^n$ you ask that for every $z_0$ with $|z_0|=1$ you have that $\sum_n a_nz_0^n=0$? Then by Abel's limit theorem, you have that $\lim_{t\to 1^{-}} f(tz_0)=\sum_{n}a_n z_0^n=0$ for every $z_0$ with $|z_0|=1$, but then for the Lusin-Privalov theorem, $f$ has to be a constant on the disc (it is enough that the set of such $z_0$ is metrically dense and of second Baire category in some arc of the unit circle).
Oct
15
answered Are differentiation and integration continuous functions?
Oct
15
comment classification of boundary values of one complex variable holomorphic functions
Sorry, what do you mean "converges"? What kind of boundary value are you considering?
Oct
15
answered Complex potential between axes & hyperbola
Oct
15
comment classification of boundary values of one complex variable holomorphic functions
what do you mean by "taken null at the boundary"? If a function is analytic on the open unit disc, continuous on its closure and zero on the boundary, then it is identically zero.
Oct
14
comment Complex potential between axes & hyperbola
No, that's NOT the question of the exercise: the "complex potential theory" does not have anything to do with Volts and electric charges, so you are probably referring to some concept of complex potential which is used in physics (like complex numbers come into play when studying circuits or holomorphic functions when studying 2d fluid dynamics), but if you don't tell us what A complex potential in general should be, we cannot tell you how to solve this problem. Weren't you given bibliographical indications for the course (Electrodynamics?)to which the exercise belong?
Oct
13
comment Complex potential between axes & hyperbola
Sorry, could you give a definition or a reference to a definition for what you call "complex potential"?
Oct
13
answered Compute $\int_\gamma\overline{\zeta} \, d\zeta$ using Cauchy’s Integral Formula
Oct
13
comment Holomorphic Sphere $ S^2$ with (-1) self intersection number
Oh, sorry, I misread … I hadn't got that "this sphere" in the two consecutive sentences was referred once to the exceptional divisor and once to an alleged "shift" of that...
Oct
13
comment Holomorphic Sphere $ S^2$ with (-1) self intersection number
Sorry, what do you mean by "is not a complex submanifold"? It is for sure an analytic subspace, as it is locally given as the zero set of holomorphic functions, then it is also smooth ...
Oct
12
answered Deriving $\frac{d}{dz} = \frac{1}{2}(\frac{d}{dx}-i\frac{d}{dy})$ Intuitively
Oct
12
answered Vanishing of Nijenhuis tensor given complex linearity?
Oct
12
answered Stupidly simple geometry problem I can't do
Oct
11
comment Surjectivity of a map $D^{2n} \to \mathbb{CP}^n$
If you look at the formula, he is actually using $\sqrt{1-\|z\|^2}$ ...