List questions from p-adic-number-theory

Published on 30 Oct 2018 - 16:38

60

Views

To prove that for $\alpha \in \mathbb{Z}_p$, $\alpha^{p^n} \equiv \alpha^{p^{n-1}}\ \text{mod}p^n$ for all $n \in \mathbb{N}$

Published on 31 Oct 2018 - 23:03

296

Views

about the p-adic logarithm

Published on 02 Nov 2018 - 11:24

148

Views

Fallacy in arguments allegedly proving the irrationality and transcendence of $\pi$ and $e$ respectively

Published on 04 Nov 2018 - 20:56

697

Views

Hensel lemma - generalization?

Published on 22 Mar 2026 - 18:26

307

Views

Relation between local and global inertia/ramification degrees

Published on 25 Mar 2026 - 4:36

107

Views

Determining the Prime Order of a Prime Power Factorial

Published on 05 Nov 2018 - 15:39

256

Views

Existence/uniqueness of the Teichmuller map for p-adic integers

Published on 07 Nov 2018 - 18:33

389

Views

Any multiplicative character $χ: \mathbb{Z}/p\mathbb{Z} \to Z_p$ is a power of the Teichmuller character

Published on 23 Feb 2026 - 0:51

148

Views

Convergence of a $p$ - adic power series

Published on 08 Nov 2018 - 16:33

95

Views

Multiplicative Group of $p$ - adic Power Series

Published on 09 Nov 2018 - 0:14

327

Views

(Sanity check) the adic spectrum $\operatorname{Spa}(\mathbb{Z}, \mathbb{Z})$

Published on 23 Mar 2026 - 12:06

140

Views

Choice of a square root in $\mathbb{Q}_7$

Published on 12 Nov 2018 - 0:27

297

Views

Uniqueness in Weierstraß p-adic preparation theorem

Published on 25 Mar 2026 - 18:53

70

Views

Newton polygon : Show that precisely $ l$ of the $ \lambda_i$ are equal to $ \lambda$

Published on 25 Mar 2026 - 6:00

List Question

Root of power $p$ from $1$ in the field of $p$-adic numbers

To prove that for $\alpha \in \mathbb{Z}_p$, $\alpha^{p^n} \equiv \alpha^{p^{n-1}}\ \text{mod}p^n$ for all $n \in \mathbb{N}$

about the p-adic logarithm

Fallacy in arguments allegedly proving the irrationality and transcendence of $\pi$ and $e$ respectively

Hensel lemma - generalization?

Relation between local and global inertia/ramification degrees

Determining the Prime Order of a Prime Power Factorial

Existence/uniqueness of the Teichmuller map for p-adic integers

Any multiplicative character $χ: \mathbb{Z}/p\mathbb{Z} \to Z_p$ is a power of the Teichmuller character

Convergence of a $p$ - adic power series

Multiplicative Group of $p$ - adic Power Series

(Sanity check) the adic spectrum $\operatorname{Spa}(\mathbb{Z}, \mathbb{Z})$

Choice of a square root in $\mathbb{Q}_7$

Uniqueness in Weierstraß p-adic preparation theorem

Newton polygon : Show that precisely $ l$ of the $ \lambda_i$ are equal to $ \lambda$

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