User Adrián Barquero

58 votes

20 answers

14k views

Interesting results easily achieved using complex numbers

asked Sep 18, 2010 at 23:54

46 votes

1 answer

5k views

Relation between the Dedekind Zeta Function and Quadratic Reciprocity

asked Apr 14, 2011 at 16:37

38 votes

1 answer

1k views

Geometric intuition behind The Mordell Conjecture

asked Apr 28, 2011 at 18:15

34 votes

5 answers

3k views

Why is it "easier" to work with function fields than with algebraic number fields?

asked Jul 21, 2011 at 3:07

32 votes

4 answers

6k views

When is an elliptic integral expressible in terms of elementary functions?

asked Dec 28, 2010 at 17:02

29 votes

7 answers

6k views

Why in an inconsistent axiom system every statement is true? (For Dummies)

asked Apr 2, 2011 at 2:34

21 votes

1 answer

4k views

Proving that the genus of a nonsingular plane curve is $\frac{(d-1)(d-2)}{2}$

asked Jun 15, 2011 at 2:20

19 votes

2 answers

1k views

Convergence of the infinite product $\prod_{n = 1}^{\infty} \frac{z - \alpha_n}{z - \beta_n}$

asked Mar 5, 2012 at 2:54

19 votes

2 answers

659 views

Which results depend on the irrationality of $\pi$?

asked May 1, 2012 at 0:19

17 votes

2 answers

2k views

Is the real locus of an elliptic curve the intersection of a torus with a plane?

asked May 22, 2011 at 1:51

15 votes

2 answers

3k views

Finding the norm in the cyclotomic field $\mathbb{Q}(e^{2\pi i / 5})$

asked Mar 3, 2011 at 17:45

15 votes

1 answer

2k views

How to compute the complex integral $\int_{\gamma} e^{\frac{1}{z^2 - 1}}\sin{\pi z} \, \mathrm dz$?

asked Aug 4, 2012 at 2:43

12 votes

1 answer

1k views

How to compute the order $\text{ord}_P (f)$ for $f \in K(C)$

asked Jun 22, 2011 at 22:54

9 votes

1 answer

274 views

Finding the least element of the greatest elements of certain subsets of the natural numbers

asked Dec 1, 2010 at 19:18

9 votes

1 answer

1k views

How to show that the entire function $f(z) = z^2 + \cos{z}$ has range all of $\mathbb{C}$?

asked Mar 12, 2012 at 23:35

9 votes

1 answer

3k views

A Number Field that's Galois over $\mathbb{Q}$ is either totally real or totally imaginary

asked Apr 15, 2012 at 17:23

9 votes

4 answers

3k views

Explicit examples of infinitely many irreducible polynomials in k[x]

asked Oct 5, 2011 at 18:45

8 votes

1 answer

1k views

Two conformal maps $\phi_i : \Omega \to \Omega$ are identical if they coincide at two different points

asked Dec 5, 2011 at 8:04

8 votes

1 answer

310 views

Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$

asked Sep 15, 2011 at 16:07

8 votes

1 answer

3k views

$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$

asked Jul 6, 2012 at 4:13

7 votes

1 answer

3k views

Proving that if $\cos{x} = \cos{y}$ and $\sin{x} = \sin{y}$ then $x-y = 2\pi n$ for some $n\in \mathbb{Z}$

asked Sep 4, 2011 at 16:42

7 votes

2 answers

1k views

The genus of an algebraic curve is invariant under isomorphisms

asked Jun 19, 2011 at 16:16

7 votes

1 answer

157 views

Proving that $\{ f_a \}_{a \in A}$ satisfying $\int \limits_{0}^{2\pi} |f_a(e^{i \phi})|^{1/2} d\phi \leq 1$ is a normal family in $\mathbb{D}$

asked Jul 19, 2013 at 3:26

6 votes

1 answer

258 views

Proving convergence of a Hilbert modular theta function $\vartheta(z):= \sum\limits_{x \in \mathcal{O}_F} e^{\pi i \operatorname{Tr}(x^2 z)}$

asked May 21, 2013 at 3:22

6 votes

3 answers

391 views

Proving that $\sum\limits_{n = 0}^{2013} a_n z^n \neq 0$ if $a_0 > a_1 > \dots > a_{2013} > 0$ and $|z| \leq 1$

asked Jul 7, 2013 at 23:08

5 votes

1 answer

550 views

An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$

asked Apr 27, 2012 at 16:43

5 votes

2 answers

988 views

$F, G \in k[X_1, \dots , X_n]$ homogeneous of degrees $r$ and $r+1$ $\implies$ $F+G$ is irreducible

asked Jul 16, 2012 at 0:14

5 votes

2 answers

2k views

Continuity of Rational Functions on the Riemann Sphere $\hat{\mathbb{C}}$

asked Nov 21, 2010 at 17:20

5 votes

1 answer

166 views

If $A, B, C$ are finitely generated $\mathbb{Z}/{p^n}\mathbb{Z}$-modules such that $A \oplus B \simeq A \oplus C$, then $B \simeq C$

asked Aug 1, 2013 at 19:29

4 votes

1 answer

1k views

Equivalent definitions of Hermite polynomials

asked Feb 17, 2014 at 20:26

Stack Exchange Network

41 Questions

Interesting results easily achieved using complex numbers

Relation between the Dedekind Zeta Function and Quadratic Reciprocity

Geometric intuition behind The Mordell Conjecture

Why is it "easier" to work with function fields than with algebraic number fields?

When is an elliptic integral expressible in terms of elementary functions?

Why in an inconsistent axiom system every statement is true? (For Dummies)

Proving that the genus of a nonsingular plane curve is $\frac{(d-1)(d-2)}{2}$

Convergence of the infinite product $\prod_{n = 1}^{\infty} \frac{z - \alpha_n}{z - \beta_n}$

Which results depend on the irrationality of $\pi$?

Is the real locus of an elliptic curve the intersection of a torus with a plane?

Finding the norm in the cyclotomic field $\mathbb{Q}(e^{2\pi i / 5})$

How to compute the complex integral $\int_{\gamma} e^{\frac{1}{z^2 - 1}}\sin{\pi z} \, \mathrm dz$?

How to compute the order $\text{ord}_P (f)$ for $f \in K(C)$

Finding the least element of the greatest elements of certain subsets of the natural numbers

How to show that the entire function $f(z) = z^2 + \cos{z}$ has range all of $\mathbb{C}$?

A Number Field that's Galois over $\mathbb{Q}$ is either totally real or totally imaginary

Explicit examples of infinitely many irreducible polynomials in k[x]

Two conformal maps $\phi_i : \Omega \to \Omega$ are identical if they coincide at two different points

Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$

$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$

Proving that if $\cos{x} = \cos{y}$ and $\sin{x} = \sin{y}$ then $x-y = 2\pi n$ for some $n\in \mathbb{Z}$

The genus of an algebraic curve is invariant under isomorphisms

Proving that $\{ f_a \}_{a \in A}$ satisfying $\int \limits_{0}^{2\pi} |f_a(e^{i \phi})|^{1/2} d\phi \leq 1$ is a normal family in $\mathbb{D}$

Proving convergence of a Hilbert modular theta function $\vartheta(z):= \sum\limits_{x \in \mathcal{O}_F} e^{\pi i \operatorname{Tr}(x^2 z)}$

Proving that $\sum\limits_{n = 0}^{2013} a_n z^n \neq 0$ if $a_0 > a_1 > \dots > a_{2013} > 0$ and $|z| \leq 1$

An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$

$F, G \in k[X_1, \dots , X_n]$ homogeneous of degrees $r$ and $r+1$ $\implies$ $F+G$ is irreducible

Continuity of Rational Functions on the Riemann Sphere $\hat{\mathbb{C}}$

If $A, B, C$ are finitely generated $\mathbb{Z}/{p^n}\mathbb{Z}$-modules such that $A \oplus B \simeq A \oplus C$, then $B \simeq C$

Equivalent definitions of Hermite polynomials