User Vik78

13 votes

5 answers

2k views

Applications of graph theory to algebra?

asked Feb 18, 2016 at 4:38

13 votes

3 answers

2k views

Theorems that give sufficient condition for a $C^{\infty}$ function to be analytic

asked Jan 3, 2017 at 2:43

11 votes

1 answer

454 views

Most general form of Cayley's theorem?

asked Mar 2, 2016 at 0:47

11 votes

2 answers

2k views

Asymptotic expression for sum of first n prime numbers?

asked Mar 11, 2016 at 20:16

10 votes

4 answers

2k views

Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$

asked Oct 11, 2016 at 3:31

6 votes

6 answers

6k views

Find $\int_0^{2\pi}\frac1{5-4\cos x}\ dx$

asked Sep 27, 2016 at 0:42

6 votes

4 answers

342 views

Does $\sum_{n = 2}^{\infty} [\zeta(n) - 1]$ converge?

asked Sep 16, 2016 at 22:01

5 votes

1 answer

88 views

I know Galois theory is used to study fields using properties of groups. Is it ever used to study groups using properties of fields?

asked Apr 10, 2016 at 21:33

5 votes

2 answers

2k views

Significance of the Riemann hypothesis to algebraic number theory?

asked Apr 29, 2016 at 20:23

5 votes

0 answers

200 views

Is there a conceptual proof that $A_n$ is simple for $n \ge 5$, or that it is the only nontrivial normal subgroup of $S_n$? [closed]

asked Aug 13, 2022 at 6:44

5 votes

0 answers

91 views

Class groups of function fields of Riemann surfaces

asked Mar 4, 2023 at 1:32

4 votes

2 answers

387 views

Seeming gap in Hartshorne's Algebraic Geometry, proof of Proposition 1.10

asked Feb 17, 2022 at 16:59

4 votes

1 answer

472 views

If more than one prime number satisfies a given congruence, must an infinite number of primes satisfy that congruence?

asked Mar 18, 2016 at 2:50

4 votes

2 answers

254 views

Is inversion ever a field automorphism? [closed]

asked Mar 2, 2016 at 14:11

4 votes

0 answers

65 views

Is there a name for this graph-theoretic concept?

asked Feb 21, 2016 at 16:09

4 votes

4 answers

320 views

Groups that are not direct products of other groups?

asked Jan 17, 2016 at 2:43

4 votes

1 answer

560 views

Does there always exist a polygonal path between any two points in the interior of a rectifiable Jordan curve?

asked Sep 28, 2016 at 2:39

4 votes

2 answers

806 views

Does a power series always have a singularity on its radius of convergence?

asked Oct 14, 2016 at 17:36

4 votes

2 answers

367 views

Can someone give an example of an ideal $I \subset R= \Bbb{Z}[x_1,...x_n]$ with $R /I \cong \Bbb{Q}$? [duplicate]

asked Jan 17, 2017 at 20:59

3 votes

1 answer

201 views

Notation reference: what does $\hat{dx}$ mean, where $dx$ is a differential form?

asked Oct 9, 2017 at 3:20

3 votes

1 answer

76 views

Is there an interesting example of a chaotic dynamical system on $\widehat{\mathbb{C}}^n$, where $\widehat{\mathbb{C}}$ is the Riemann sphere?

asked Jan 12, 2022 at 22:10

3 votes

1 answer

262 views

Question from Herstein's Topics in Algebra on Sylow theory

asked Aug 29, 2016 at 17:05

3 votes

0 answers

197 views

The natural numbers form a distributive lattice under gcd and lcm. In arbitrary gcd domains, does gcd distribute over lcm?

asked Feb 1, 2016 at 18:32

3 votes

1 answer

179 views

Suppose A is a principal ideal domain with every ideal of finite index. Must A be a Euclidean domain?

asked Feb 3, 2016 at 16:29

3 votes

1 answer

170 views

Integral of $x^{-x}$ from $0$ to infinity $=$ $2$? [duplicate]

asked Feb 22, 2016 at 4:42

3 votes

0 answers

424 views

Proving that primes of the form $4k + 1$ are not Gaussian primes

asked Mar 7, 2016 at 3:14

3 votes

2 answers

1k views

What are some applications of large cardinals?

asked Apr 23, 2016 at 3:25

2 votes

0 answers

42 views

Can anyone give an example of a set of numbers with arithmetic density that doesn't converge to a limit?

asked May 23, 2016 at 2:12

2 votes

1 answer

275 views

How are Gauss sums the analogue of the gamma function for finite fields?

asked May 3, 2016 at 0:33

2 votes

0 answers

103 views

Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$. [duplicate]

asked May 5, 2016 at 1:01

Stack Exchange Network

87 Questions

Applications of graph theory to algebra?

Theorems that give sufficient condition for a $C^{\infty}$ function to be analytic

Most general form of Cayley's theorem?

Asymptotic expression for sum of first n prime numbers?

Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$

Find $\int_0^{2\pi}\frac1{5-4\cos x}\ dx$

Does $\sum_{n = 2}^{\infty} [\zeta(n) - 1]$ converge?

I know Galois theory is used to study fields using properties of groups. Is it ever used to study groups using properties of fields?

Significance of the Riemann hypothesis to algebraic number theory?

Is there a conceptual proof that $A_n$ is simple for $n \ge 5$, or that it is the only nontrivial normal subgroup of $S_n$? [closed]

Class groups of function fields of Riemann surfaces

Seeming gap in Hartshorne's Algebraic Geometry, proof of Proposition 1.10

If more than one prime number satisfies a given congruence, must an infinite number of primes satisfy that congruence?

Is inversion ever a field automorphism? [closed]

Is there a name for this graph-theoretic concept?

Groups that are not direct products of other groups?

Does there always exist a polygonal path between any two points in the interior of a rectifiable Jordan curve?

Does a power series always have a singularity on its radius of convergence?

Can someone give an example of an ideal $I \subset R= \Bbb{Z}[x_1,...x_n]$ with $R /I \cong \Bbb{Q}$? [duplicate]

Notation reference: what does $\hat{dx}$ mean, where $dx$ is a differential form?

Is there an interesting example of a chaotic dynamical system on $\widehat{\mathbb{C}}^n$, where $\widehat{\mathbb{C}}$ is the Riemann sphere?

Question from Herstein's Topics in Algebra on Sylow theory

The natural numbers form a distributive lattice under gcd and lcm. In arbitrary gcd domains, does gcd distribute over lcm?

Suppose A is a principal ideal domain with every ideal of finite index. Must A be a Euclidean domain?

Integral of $x^{-x}$ from $0$ to infinity $=$ $2$? [duplicate]

Proving that primes of the form $4k + 1$ are not Gaussian primes

What are some applications of large cardinals?

Can anyone give an example of a set of numbers with arithmetic density that doesn't converge to a limit?

How are Gauss sums the analogue of the gamma function for finite fields?

Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$. [duplicate]