Question

Does $(6-\sqrt{37})y^2=(6-\sqrt{37})^2-68x^4$ have solution over $\Bbb{Q}_2(\sqrt{37})=\Bbb{Q}_2(\sqrt{5})$ and over $\Bbb{Q}_{17}(\sqrt{37})$?

score 73 · Answer 1 · 2023-06-28 11:10:45

73

Views

Does $(6-\sqrt{37})y^2=(6-\sqrt{37})^2-68x^4$ have solution over $\Bbb{Q}_2(\sqrt{37})=\Bbb{Q}_2(\sqrt{5})$ and over $\Bbb{Q}_{17}(\sqrt{37})$?

Published on 28 Jun 2023 - 11:10

score 111 · Answer 2 · 2026-03-25 01:16:37

111

Views

When is the zero set of a multivariate $p$-adic power series algebraic?

Published on 25 Mar 2026 - 1:16

score 74 · Answer 3 · 2023-06-30 14:01:26

74

Views

Quasi-connected set

Published on 30 Jun 2023 - 14:01

score 100 · Answer 4 · 2026-03-26 04:35:05

100

Views

Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$?

Published on 26 Mar 2026 - 4:35

score 89 · Answer 5 · 2023-07-02 19:11:51

89

Views

Why $\forall n \in \mathbb{Z}_{\geq 1}$ it is $n^{-1} \leq |n|_*$?

Published on 02 Jul 2023 - 19:11

score 46 · Answer 6 · 2023-07-03 23:18:15

46

Views

Book references for p-adic Fourier theory

Published on 03 Jul 2023 - 23:18

score 97 · Answer 7 · 2026-03-26 20:44:02

97

Views

Prove $v_p(a^2+b^2)$ is even for $a, b\in\mathbb{Z}_p$ and $p\equiv 3\pmod 4$.

Published on 26 Mar 2026 - 20:44

score 138 · Answer 8 · 2023-07-04 04:39:38

138

Views

Does $17x^4+y^2=-1$ have solution in $\Bbb{Q}_2$?

Published on 04 Jul 2023 - 4:39

score 160 · Answer 9 · 2023-07-04 12:37:31

160

Views

Does $x^2+y^2=-1$ have solution in $p$ adic number field?

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score 54 · Answer 10 · 2023-07-05 13:17:35

54

Views

Surjection of the perfection of two characteristic $p$ rings

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score 80 · Answer 11 · 2023-07-05 14:31:06

80

Views

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score 62 · Answer 12 · 2023-07-07 15:11:39

62

Views

Does this map send every algebraic number to a periodic 2-adic?

Published on 07 Jul 2023 - 15:11

score 82 · Answer 13 · 2026-03-29 08:35:51

82

Views

Relation of Class numbers and Special Values of zeta functions

Published on 29 Mar 2026 - 8:35

score 45 · Answer 14 · 2026-03-27 21:02:27

45

Views

The p-adic value of Dirichlet L-function at 1

Published on 27 Mar 2026 - 21:02

score 77 · Answer 15 · 2023-07-10 19:58:50

77

Views

On Kato's proof that first Iwasawa cohomology is free

Published on 10 Jul 2023 - 19:58

List Question

Does $(6-\sqrt{37})y^2=(6-\sqrt{37})^2-68x^4$ have solution over $\Bbb{Q}_2(\sqrt{37})=\Bbb{Q}_2(\sqrt{5})$ and over $\Bbb{Q}_{17}(\sqrt{37})$?

When is the zero set of a multivariate $p$-adic power series algebraic?

Quasi-connected set

Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$?

Why $\forall n \in \mathbb{Z}_{\geq 1}$ it is $n^{-1} \leq |n|_*$?

Book references for p-adic Fourier theory

Prove $v_p(a^2+b^2)$ is even for $a, b\in\mathbb{Z}_p$ and $p\equiv 3\pmod 4$.

Does $17x^4+y^2=-1$ have solution in $\Bbb{Q}_2$?

Does $x^2+y^2=-1$ have solution in $p$ adic number field?

Surjection of the perfection of two characteristic $p$ rings

When are $a$-adic numbers torsion-free?

Does this map send every algebraic number to a periodic 2-adic?

Relation of Class numbers and Special Values of zeta functions

The p-adic value of Dirichlet L-function at 1

On Kato's proof that first Iwasawa cohomology is free

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