Question

Do there exist elements in cyclotomic fields with certain absolute value?

score 92 · Answer 1 · 2021-03-11 16:31:37

92

Views

Do there exist elements in cyclotomic fields with certain absolute value?

Published on 11 Mar 2021 - 16:31

score 150 · Answer 2 · 2021-03-16 11:14:03

150

Views

Intersection of cyclotomic fields over an arbitary number field

Published on 16 Mar 2021 - 11:14

score 25 · Answer 3 · 2021-03-27 02:01:59

25

Views

Algorithm for computing residues of Galois conjugates of an integer in a prime-power cyclotomic field

Published on 27 Mar 2021 - 2:01

score 32 · Answer 4 · 2021-04-07 07:43:47

32

Views

$e^{2\pi i/k}\mapsto e^{2\pi i m/k}$ automorphism on the cyclotomic field $\mathbb{Q}(e^{2\pi i/k})$

Published on 07 Apr 2021 - 7:43

score 36 · Answer 5 · 2021-04-13 14:34:32

36

Views

Compute some of powers of root of unity in $\Bbb C$

Published on 13 Apr 2021 - 14:34

score 62 · Answer 6 · 2021-04-16 17:46:34

62

Views

Proof of Iwasawa's theorem

Published on 16 Apr 2021 - 17:46

score 42 · Answer 7 · 2021-04-21 00:14:17

42

Views

How do you find a basis for $\mathbb{C}$ as a vector space over $\mathbb{Q}(\zeta_n)$?

Published on 21 Apr 2021 - 0:14

score 122 · Answer 8 · 2021-04-21 09:47:34

122

Views

Ramification question in compositum of cyclotomic and degree 5 extension.

Published on 21 Apr 2021 - 9:47

score 589 · Answer 9 · 2021-04-21 16:31:38

589

Views

Quadratic subfields of the cyclotomic field $\mathbb{Q}(\zeta_{14})$

Published on 21 Apr 2021 - 16:31

score 105 · Answer 10 · 2021-05-02 11:18:04

105

Views

show that there exists a unique subfield $H$ of $\mathbb{Q}(\xi_9)$ such that $[H:\mathbb{Q}]=2$.

Published on 02 May 2021 - 11:18

score 67 · Answer 11 · 2021-05-28 11:30:22

67

Views

On the quintic power residue symbol

Published on 28 May 2021 - 11:30

score 54 · Answer 12 · 2021-06-03 12:39:04

54

Views

How to prove that $\Pi_{1 \leq j \leq p^n, p \nmid j}((\zeta_{p^n}^j)^{p^{n-1}}-1) = p^{p^{n-1}}$?

Published on 03 Jun 2021 - 12:39

score 303 · Answer 13 · 2021-06-07 05:21:16

303

Views

Is the absolute value of the sum of six of the 16th roots of unity ever a nonzero integer?

Published on 07 Jun 2021 - 5:21

score 452 · Answer 14 · 2021-06-07 12:08:57

452

Views

Splitting field of $x^4 + 1$ over $Q$

Published on 07 Jun 2021 - 12:08

score 58 · Answer 15 · 2021-06-09 16:02:57

58

Views

How to use the Bezout identity in the $mn$-th roots of unity?

Published on 09 Jun 2021 - 16:02

List Question

Do there exist elements in cyclotomic fields with certain absolute value?

Intersection of cyclotomic fields over an arbitary number field

Algorithm for computing residues of Galois conjugates of an integer in a prime-power cyclotomic field

$e^{2\pi i/k}\mapsto e^{2\pi i m/k}$ automorphism on the cyclotomic field $\mathbb{Q}(e^{2\pi i/k})$

Compute some of powers of root of unity in $\Bbb C$

Proof of Iwasawa's theorem

How do you find a basis for $\mathbb{C}$ as a vector space over $\mathbb{Q}(\zeta_n)$?

Ramification question in compositum of cyclotomic and degree 5 extension.

Quadratic subfields of the cyclotomic field $\mathbb{Q}(\zeta_{14})$

show that there exists a unique subfield $H$ of $\mathbb{Q}(\xi_9)$ such that $[H:\mathbb{Q}]=2$.

On the quintic power residue symbol

How to prove that $\Pi_{1 \leq j \leq p^n, p \nmid j}((\zeta_{p^n}^j)^{p^{n-1}}-1) = p^{p^{n-1}}$?

Is the absolute value of the sum of six of the 16th roots of unity ever a nonzero integer?

Splitting field of $x^4 + 1$ over $Q$

How to use the Bezout identity in the $mn$-th roots of unity?

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