List questions from p-adic-number-theory

Published on 06 Nov 2012 - 23:24

186

Views

Show that $x^4+1$ is reducible in p-adic numbers $\mathbb{Q}_p$ for p>2 prime.

Published on 12 Nov 2012 - 21:46

591

Views

Galois group of maximal $p$-extension of $\mathbb{Q}_l(\zeta_p)$?

Published on 16 Nov 2012 - 17:12

105

Views

Powers of $\Bbb Z_p\cap \Bbb Q$ on $1+x\Bbb F_q[[x]]$

Published on 17 Nov 2012 - 3:47

1.3k

Views

hensel's lemma for the prime 2

Published on 18 Nov 2012 - 3:04

303

Views

Cyclotomy in extensions of $\mathbb{Q}_p$

Published on 28 Nov 2012 - 17:02

873

Views

$p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.

Published on 03 Dec 2012 - 11:56

2.7k

Views

How do you take the multiplicative inverse of a p-adic number?

Published on 03 Dec 2012 - 17:16

381

Views

Quasi-linear time fully homomorphic encryption using p-adic ring homomorphism

Published on 02 Dec 2012 - 19:42

3.4k

Views

Are the p-adic integers the ring of integers of the field of p-adic numbers?

Published on 09 Dec 2012 - 3:23

183

Views

A $p$-adic "Jacobi sum" with an unramified character

Published on 12 Dec 2012 - 5:53

1k

Views

Roots of 1 in $\mathbb Q_p$

Published on 15 Dec 2012 - 12:35

713

Views

Valuation rings of complete non-archimedean fields which are not local

Published on 28 Mar 2026 - 7:00

286

Views

Preservation of being a norm under field extension

Published on 31 Dec 2012 - 21:00

440

Views

When a number is a square in the p-adic rationals - proof question (Quadratic Residues)

Published on 03 Jan 2013 - 14:18

List Question

continued fraction expression for $\sqrt{2}$ in $\mathbb{Q_7}$

Show that $x^4+1$ is reducible in p-adic numbers $\mathbb{Q}_p$ for p>2 prime.

Galois group of maximal $p$-extension of $\mathbb{Q}_l(\zeta_p)$?

Powers of $\Bbb Z_p\cap \Bbb Q$ on $1+x\Bbb F_q[[x]]$

hensel's lemma for the prime 2

Cyclotomy in extensions of $\mathbb{Q}_p$

$p$-adic unit for $p\neq 2$ is a square in $\mathbb{Z}_p$ if and only if its first digit is quadratic residue modulo $p$.

How do you take the multiplicative inverse of a p-adic number?

Quasi-linear time fully homomorphic encryption using p-adic ring homomorphism

Are the p-adic integers the ring of integers of the field of p-adic numbers?

A $p$-adic "Jacobi sum" with an unramified character

Roots of 1 in $\mathbb Q_p$

Valuation rings of complete non-archimedean fields which are not local

Preservation of being a norm under field extension

When a number is a square in the p-adic rationals - proof question (Quadratic Residues)

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