Question

If $X$ has character $\chi$ and degree $d$. Prove that $g \in N$ if and only if $\chi(g) = d$ . Hint: Show that $\chi(g)$ is a sum of roots of unity.

score 409 · Answer 1 · 2016-02-25 01:29:10

409

Views

If $X$ has character $\chi$ and degree $d$. Prove that $g \in N$ if and only if $\chi(g) = d$ . Hint: Show that $\chi(g)$ is a sum of roots of unity.

Published on 25 Feb 2016 - 1:29

score 399 · Answer 2 · 2016-02-26 22:24:55

399

Views

$ p \in Q[x] $ has as a root a fifth primitive root of unity, then every fifth primitive root of unity is a root of $p$.

Published on 26 Feb 2016 - 22:24

score 42 · Answer 3 · 2016-02-26 23:22:32

If $k \in \mathbb{N}, n={2^k} $. Probe that $w$ is a primitive nth-root of unity $\iff$ $w$ is a root of $ P_k = x^{2^{k-1}} + 1 $

score 299 · Answer 4 · 2016-03-02 16:31:32

299

Views

Find all $ z \in {\mathbb C} $ such that $z^{12}=1 $ and $ 1+z+z^2+z^3+z^4+z^5 \in {\mathbb R} $

Published on 02 Mar 2016 - 16:31

score 446 · Answer 5 · 2026-03-27 02:37:35

446

Views

roots of unity and cyclotomic polynomials over $\mathbb{F}_p$

Published on 27 Mar 2026 - 2:37

score 211 · Answer 6 · 2016-03-04 02:55:34

211

Views

Let $\zeta_n$ be the $n^{th}$ root of unity $\zeta_n=e^{2\pi i/n}$. How can I prove that $\zeta_5\notin \mathbb{Q}(\zeta_7)$?

Published on 04 Mar 2016 - 2:55

score 1.5k · Answer 7 · 2016-03-06 09:01:10

1.5k

Views

Alternating sum of roots of unity $\sum_{k=0}^{n-1}(-1)^k\omega^k$

Published on 06 Mar 2016 - 9:01

score 5.1k · Answer 8 · 2016-03-08 04:12:09

5.1k

Views

Solve for $z$ in $z^3=8i$

Published on 08 Mar 2016 - 4:12

score 216 · Answer 9 · 2016-03-09 00:59:11

216

Views

Invertibility of a certain matrix attached to a primitive root of unity.

Published on 09 Mar 2016 - 0:59

score 110 · Answer 10 · 2016-03-11 19:03:10

110

Views

sum of roots of unity multiplied by k+1

Published on 11 Mar 2016 - 19:03

score 206 · Answer 11 · 2026-03-28 22:53:32

206

Views

Finite Messy Trigonometric Sum

Published on 28 Mar 2026 - 22:53

score 226 · Answer 12 · 2016-03-21 12:51:03

226

Views

I want to find the 6th root of z which lies in a specific domain.

Published on 21 Mar 2016 - 12:51

score 3.9k · Answer 13 · 2016-03-22 03:03:59

3.9k

Views

Solve $z^4 = 1$ for all $z$ , Hence or otherwise, solve $z^4 =(z-1)^4$

Published on 22 Mar 2016 - 3:03

score 511 · Answer 14 · 2016-03-22 13:57:14

511

Views

A spiralling sequence based on integer divisors. Has anyone noticed this before?

Published on 22 Mar 2016 - 13:57

score 162 · Answer 15 · 2016-03-24 08:24:14

162

Views

The norm and the angle of the complex number $\sqrt[3]{-1}\sqrt[6]{7}$?

Published on 24 Mar 2016 - 8:24

List Question

If $X$ has character $\chi$ and degree $d$. Prove that $g \in N$ if and only if $\chi(g) = d$ . Hint: Show that $\chi(g)$ is a sum of roots of unity.

$ p \in Q[x] $ has as a root a fifth primitive root of unity, then every fifth primitive root of unity is a root of $p$.

If $k \in \mathbb{N}, n={2^k} $. Probe that $w$ is a primitive nth-root of unity $\iff$ $w$ is a root of $ P_k = x^{2^{k-1}} + 1 $

Find all $ z \in {\mathbb C} $ such that $z^{12}=1 $ and $ 1+z+z^2+z^3+z^4+z^5 \in {\mathbb R} $

roots of unity and cyclotomic polynomials over $\mathbb{F}_p$

Let $\zeta_n$ be the $n^{th}$ root of unity $\zeta_n=e^{2\pi i/n}$. How can I prove that $\zeta_5\notin \mathbb{Q}(\zeta_7)$?

Alternating sum of roots of unity $\sum_{k=0}^{n-1}(-1)^k\omega^k$

Solve for $z$ in $z^3=8i$

Invertibility of a certain matrix attached to a primitive root of unity.

sum of roots of unity multiplied by k+1

Finite Messy Trigonometric Sum

I want to find the 6th root of z which lies in a specific domain.

Solve $z^4 = 1$ for all $z$ , Hence or otherwise, solve $z^4 =(z-1)^4$

A spiralling sequence based on integer divisors. Has anyone noticed this before?

The norm and the angle of the complex number $\sqrt[3]{-1}\sqrt[6]{7}$?

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