Question

Degree of the field extension $\mathbb{Q}(\epsilon)|\mathbb{Q}(\epsilon^3)$, $\epsilon$ being a 9-primitive root of unity

score 87 · Answer 1 · 2020-04-20 17:17:17

87

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Degree of the field extension $\mathbb{Q}(\epsilon)|\mathbb{Q}(\epsilon^3)$, $\epsilon$ being a 9-primitive root of unity

Published on 20 Apr 2020 - 17:17

score 157 · Answer 2 · 2026-03-26 00:53:47

157

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what is the value of $\binom{n}{1}+\binom{n}{4}+\binom{n}{7}+\binom{n}{10}+\binom{n}{13}+\dots$

Published on 26 Mar 2026 - 0:53

score 174 · Answer 3 · 2020-04-29 05:31:25

174

Views

Evaluate $\frac{q}{1+q^2}+\frac{q^2}{1+q^4}+\frac{q^3}{1+q^6}$, where $q^7=1$ and $q\neq 1$.

Published on 29 Apr 2020 - 5:31

score 37 · Answer 4 · 2020-04-29 16:01:32

37

Views

How to find the determinant of this ${P_n^r}\times{P_n^r}$-matrix?

Published on 29 Apr 2020 - 16:01

score 28 · Answer 5 · 2020-04-30 10:09:38

28

Views

If $\mu_{p}(k)={1}$, $p$ is a prime, is the polynomial $\sum_{j=0}^{p-1}x^{j}$ irreducible over $k$?

Published on 30 Apr 2020 - 10:09

score 148 · Answer 6 · 2020-05-03 14:59:39

148

Views

Let $E(n,z)=|z+1|+|z^{2n}+1|$. Find $\displaystyle\min_{z\in\mathbb{C}} E(n,z)$.

Published on 03 May 2020 - 14:59

score 279 · Answer 7 · 2020-05-06 11:29:32

279

Views

Prove $\cos\frac{π}{9} \cos\frac{2π}{9} \cos\frac{4π}{9}=\frac{1}{8}$ with complex numbers (roots of unity)

Published on 06 May 2020 - 11:29

score 71 · Answer 8 · 2020-05-12 08:57:47

71

Views

How to show $ \Bbb Q（ζ_n,i）＝ \Bbb Q（ζ_N）$, where $ N＝LCM（n,4）$

Published on 12 May 2020 - 8:57

score 102 · Answer 9 · 2020-05-15 09:52:22

102

Views

Matrix's determinant with product and sum and root unity

Published on 15 May 2020 - 9:52

score 90 · Answer 10 · 2026-03-25 11:33:47

90

Views

Different branchs of $w^{1/3}$

Published on 25 Mar 2026 - 11:33

score 91 · Answer 11 · 2026-03-25 09:50:18

91

Views

Why does an element of the Galois group of $K(\mu_n)/K$ maps an $n$-th root of unity to another $n$-th root of unity?

Published on 25 Mar 2026 - 9:50

score 132 · Answer 12 · 2020-05-24 11:00:14

132

Views

Compute $\sum_{x\in\mathcal{N}}\sum_{y\in\mathcal{N}}\frac{1}{x+y+1}$

Published on 24 May 2020 - 11:00

score 47 · Answer 13 · 2020-05-26 21:21:18

47

Views

How do I optimize a rotation of the roots of unity?

Published on 26 May 2020 - 21:21

score 35 · Answer 14 · 2020-05-27 10:04:32

35

Views

Given eigenvectors, what is the set of eigenvalues that makes the matrix have specific coefficients?

Published on 27 May 2020 - 10:04

score 125 · Answer 15 · 2026-03-25 11:24:31

125

Views

Unit roots group is isomorphic to $\Bbb{Q}/\Bbb{Z}\left[\frac{1}{p}\right]$ in a field of characteristic $p\ge0$

Published on 25 Mar 2026 - 11:24

List Question

Degree of the field extension $\mathbb{Q}(\epsilon)|\mathbb{Q}(\epsilon^3)$, $\epsilon$ being a 9-primitive root of unity

what is the value of $\binom{n}{1}+\binom{n}{4}+\binom{n}{7}+\binom{n}{10}+\binom{n}{13}+\dots$

Evaluate $\frac{q}{1+q^2}+\frac{q^2}{1+q^4}+\frac{q^3}{1+q^6}$, where $q^7=1$ and $q\neq 1$.

How to find the determinant of this ${P_n^r}\times{P_n^r}$-matrix?

If $\mu_{p}(k)={1}$, $p$ is a prime, is the polynomial $\sum_{j=0}^{p-1}x^{j}$ irreducible over $k$?

Let $E(n,z)=|z+1|+|z^{2n}+1|$. Find $\displaystyle\min_{z\in\mathbb{C}} E(n,z)$.

Prove $\cos\frac{π}{9} \cos\frac{2π}{9} \cos\frac{4π}{9}=\frac{1}{8}$ with complex numbers (roots of unity)

How to show $ \Bbb Q（ζ_n,i）＝ \Bbb Q（ζ_N）$, where $ N＝LCM（n,4）$

Matrix's determinant with product and sum and root unity

Different branchs of $w^{1/3}$

Why does an element of the Galois group of $K(\mu_n)/K$ maps an $n$-th root of unity to another $n$-th root of unity?

Compute $\sum_{x\in\mathcal{N}}\sum_{y\in\mathcal{N}}\frac{1}{x+y+1}$

How do I optimize a rotation of the roots of unity?

Given eigenvectors, what is the set of eigenvalues that makes the matrix have specific coefficients?

Unit roots group is isomorphic to $\Bbb{Q}/\Bbb{Z}\left[\frac{1}{p}\right]$ in a field of characteristic $p\ge0$

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