Question

Algebraic integers in $p^r$-th cyclotomic field

score 238 · Answer 1 · 2026-04-15 08:08:45

238

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Algebraic integers in $p^r$-th cyclotomic field

Published on 15 Apr 2026 - 8:08

score 108 · Answer 2 · 2026-04-17 12:13:22

108

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Product involving Dirichlet characters $\prod_{i=1}^{\phi(m)}(1 - \frac{\chi_i(p)}{p^s}) =(1 - \frac{1}{p^{fs}})^{\frac{\phi(m)}{f}}$

Published on 17 Apr 2026 - 12:13

score 71 · Answer 3 · 2026-04-14 07:48:20

71

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Aside from $\langle 0 \rangle$, can a ring of algebraic integers have prime ideals that are not maximal?

Published on 14 Apr 2026 - 7:48

score 77 · Answer 4 · 2026-04-11 00:37:12

77

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Generalize a trick with Dirichlet series to algebraic number theory

Published on 11 Apr 2026 - 0:37

score 507 · Answer 5 · 2026-04-10 12:14:18

507

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Infinite Units for $\mathbb{Z}[\sqrt{7}]$

Published on 10 Apr 2026 - 12:14

score 180 · Answer 6 · 2026-04-14 14:02:10

180

Views

Convergence of roots of polynomials with coefficients in non-archimedean local field

Published on 14 Apr 2026 - 14:02

score 40 · Answer 7 · 2026-04-09 12:28:02

40

Views

Showing that $A^$ is and ideal and that "$$" is multiplicative.

Published on 09 Apr 2026 - 12:28

score 449 · Answer 8 · 2026-03-25 06:22:11

449

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Is $\mathcal{O}_K$ always isomorphic to $\mathbb{Z}[X]/(f(x))$, for some irreducible polynomial $f(x)$?

Published on 25 Mar 2026 - 6:22

score 357 · Answer 9 · 2026-04-15 11:46:30

357

Views

Describing $Spec(\mathcal{O}_K[X])$

Published on 15 Apr 2026 - 11:46

score 553 · Answer 10 · 2026-04-10 06:05:28

553

Views

Picard group of $\mathbb Z[\sqrt{-5}]$

Published on 10 Apr 2026 - 6:05

score 657 · Answer 11 · 2026-04-12 20:59:59

657

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Inertia groups of cyclotomic field extension

Published on 12 Apr 2026 - 20:59

score 77 · Answer 12 · 2026-04-11 03:22:44

77

Views

Measurability in the proof of Minkowski's Bound for calculating the Class Number?

Published on 11 Apr 2026 - 3:22

score 546 · Answer 13 · 2026-04-16 21:38:04

546

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If $p\equiv 1,9 \pmod{20}$ is a prime number, then there exist $a,b\in\mathbb{Z}$ such that $p=a^{2}+5b^{2}$.

Published on 16 Apr 2026 - 21:38

score 88 · Answer 14 · 2026-04-15 22:46:14

88

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Compute the index of $\mathbf{Z}[\alpha]$ in $\mathbf{Z}[\alpha,\beta,\gamma]$

Published on 15 Apr 2026 - 22:46

score 2.3k · Answer 15 · 2026-04-17 13:55:34

2.3k

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Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$

Published on 17 Apr 2026 - 13:55

List Question

Algebraic integers in $p^r$-th cyclotomic field

Product involving Dirichlet characters $\prod_{i=1}^{\phi(m)}(1 - \frac{\chi_i(p)}{p^s}) =(1 - \frac{1}{p^{fs}})^{\frac{\phi(m)}{f}}$

Aside from $\langle 0 \rangle$, can a ring of algebraic integers have prime ideals that are not maximal?

Generalize a trick with Dirichlet series to algebraic number theory

Infinite Units for $\mathbb{Z}[\sqrt{7}]$

Convergence of roots of polynomials with coefficients in non-archimedean local field

Showing that $A^$ is and ideal and that "$$" is multiplicative.

Is $\mathcal{O}_K$ always isomorphic to $\mathbb{Z}[X]/(f(x))$, for some irreducible polynomial $f(x)$?

Describing $Spec(\mathcal{O}_K[X])$

Picard group of $\mathbb Z[\sqrt{-5}]$

Inertia groups of cyclotomic field extension

Measurability in the proof of Minkowski's Bound for calculating the Class Number?

If $p\equiv 1,9 \pmod{20}$ is a prime number, then there exist $a,b\in\mathbb{Z}$ such that $p=a^{2}+5b^{2}$.

Compute the index of $\mathbf{Z}[\alpha]$ in $\mathbf{Z}[\alpha,\beta,\gamma]$

Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$

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