List questions from cyclotomic-fields

Published on 17 Mar 2026 - 0:54

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Question about the Cyclotomic polynomial and Cyclotomic field.

Published on 21 Mar 2026 - 10:14

242

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Is $\sqrt[3]5+\sqrt[3]7$ contained in a cyclotomic extension?

Published on 16 Jun 2018 - 11:29

160

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How to show that $\mathrm{Gal}(\Bbb Q(\xi_{p^n})/\Bbb Q(\xi_{p^m}))$ is cyclic?

Published on 21 Jun 2018 - 11:41

1.4k

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Root of unity belongs to Z/qZ. How?

Published on 21 Mar 2026 - 17:31

256

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If $n$ divides $m$, prove that $\mathbb{Q}(\zeta_{n}) \subset \mathbb{Q}(\zeta_{m})$

Published on 29 Jun 2018 - 21:31

87

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Let $l:=\text{lcm}(n,m)$. Show $\mathbb Q(\zeta_n,\zeta_m)=\mathbb Q(\zeta_l)$.

Published on 02 Jul 2018 - 13:50

45

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class number for special cyclotomic fields

Published on 17 Mar 2026 - 4:50

69

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Is $h(n) < 2^n$ for all $n$? ($n$th cyclotomic field class number growth)

Published on 19 Jul 2018 - 19:41

973

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Calculating class numbers

Published on 19 Mar 2026 - 23:29

106

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Minimal polynomial generators of aurifeuillan factors cyclotomic polynomials

Published on 22 Mar 2026 - 11:35

142

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Minkowski bound of $229$-th cyclotomic field

Published on 17 Mar 2026 - 13:23

124

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Primes $p=1\pmod 5$

Published on 16 Mar 2026 - 21:13

118

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The Stickelberger relation in Ireland&Rosen's Number Theory book

Published on 17 Mar 2026 - 20:45

445

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$\mathbb Q(\zeta_m)\cap\mathbb Q(\zeta_n)=\mathbb Q(\zeta_d)$

Published on 04 Oct 2018 - 13:58

List Question

Cyclic units in $Z_p$ towers

Question about the Cyclotomic polynomial and Cyclotomic field.

Is $\sqrt[3]5+\sqrt[3]7$ contained in a cyclotomic extension?

How to show that $\mathrm{Gal}(\Bbb Q(\xi_{p^n})/\Bbb Q(\xi_{p^m}))$ is cyclic?

Root of unity belongs to Z/qZ. How?

If $n$ divides $m$, prove that $\mathbb{Q}(\zeta_{n}) \subset \mathbb{Q}(\zeta_{m})$

Let $l:=\text{lcm}(n,m)$. Show $\mathbb Q(\zeta_n,\zeta_m)=\mathbb Q(\zeta_l)$.

class number for special cyclotomic fields

Is $h(n) < 2^n$ for all $n$? ($n$th cyclotomic field class number growth)

Calculating class numbers

Minimal polynomial generators of aurifeuillan factors cyclotomic polynomials

Minkowski bound of $229$-th cyclotomic field

Primes $p=1\pmod 5$

The Stickelberger relation in Ireland&Rosen's Number Theory book

$\mathbb Q(\zeta_m)\cap\mathbb Q(\zeta_n)=\mathbb Q(\zeta_d)$

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