List questions from p-adic-number-theory

Published on 20 Apr 2017 - 1:07

70

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Is that a convention that $\frac{1}{1-x}=1+x+x^2+...$ in $\mathbb{Q}_p$ or $p$-adic number theory?

Published on 20 Apr 2017 - 3:22

1k

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$\mathbb{Q}_2$ and its quadratic field extensions

Published on 22 Apr 2017 - 14:58

428

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Tensor product of algebraic number field with p-adic field

Published on 23 Apr 2017 - 20:18

49

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If $\mathbb{Q}_p(\sqrt{a}) \cong \mathbb{Q}_p(\sqrt{b})$ ($a,b$ non-squares), then $a/b$ is a square?

Published on 25 Apr 2017 - 10:18

452

Views

A $p$-adic unit is an $n^{th}$ power if it is congruent to a $n^{th}$ power mod $m$ (Eisenbud exercise)

Published on 25 Mar 2026 - 11:04

224

Views

What triangles do the $p-$adic numbers generate?

Published on 27 Apr 2017 - 19:44

716

Views

Do the following series converge in p-adic numbers?

Published on 01 May 2017 - 16:50

230

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Why is $x^2+1$ irreducible in $\mathbb{Q}_2[x]$.

Published on 01 May 2017 - 18:40

514

Views

isomorphic extension fields of the $p$-adic numbers

Published on 01 Apr 2026 - 20:24

161

Views

Computing the quotient $\mathbb{Q}_p[x]/(x^2 + 1)$

Published on 25 Mar 2026 - 7:41

652

Views

What is the group structure of 3-adic group of the cubes of units?

Published on 03 May 2017 - 4:48

144

Views

order of $\mathbb{Z}_3^/(\mathbb{Z}_3^)^3$

Published on 03 May 2017 - 15:46

192

Views

square root of $-1$ in $\mathbb{Q}_p$

Published on 25 Mar 2026 - 7:49

323

Views

Squares in $\mathbb{Q}_p \bmod p$ (p-adic numbers)

Published on 25 Mar 2026 - 7:41

List Question

How to show if $x\in\mathbb{Q}$ ,then there exists $N \ge0$ such that $p^Nx\in\mathbb{Z}_p$?

Is that a convention that $\frac{1}{1-x}=1+x+x^2+...$ in $\mathbb{Q}_p$ or $p$-adic number theory?

$\mathbb{Q}_2$ and its quadratic field extensions

Tensor product of algebraic number field with p-adic field

If $\mathbb{Q}_p(\sqrt{a}) \cong \mathbb{Q}_p(\sqrt{b})$ ($a,b$ non-squares), then $a/b$ is a square?

A $p$-adic unit is an $n^{th}$ power if it is congruent to a $n^{th}$ power mod $m$ (Eisenbud exercise)

What triangles do the $p-$adic numbers generate?

Do the following series converge in p-adic numbers?

Why is $x^2+1$ irreducible in $\mathbb{Q}_2[x]$.

isomorphic extension fields of the $p$-adic numbers

Computing the quotient $\mathbb{Q}_p[x]/(x^2 + 1)$

What is the group structure of 3-adic group of the cubes of units?

order of $\mathbb{Z}_3^/(\mathbb{Z}_3^)^3$

square root of $-1$ in $\mathbb{Q}_p$

Squares in $\mathbb{Q}_p \bmod p$ (p-adic numbers)

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