Timeline for Is $e^p\in\mathbb{Q}_p$ known to be transcendental?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2012 at 21:29 | comment | added | Felipe Voloch | @Gerald. No cube root. If $a \in \mathbb{Q}_3, a \equiv 1 \mod 3$, then $a^3 \equiv 1 \mod 9$. On the other hand, $\exp(3) \equiv 1+3 \mod 9$. | |
| Nov 3, 2012 at 20:19 | comment | added | Gerald Edgar | So, $\exp(3)$ is a $3$-adic number. Does it have (one or more) cube roots in $\mathbb Q_3$ ? And if so, is one of them naturally singled out as something to call $e$ ? If not, perhaps write $\exp(3)$ and not $e^3$ then... | |
| Nov 3, 2012 at 16:41 | vote | accept | 36min | ||
| Nov 3, 2012 at 16:39 | vote | accept | 36min | ||
| Nov 3, 2012 at 16:40 | |||||
| Nov 3, 2012 at 16:25 | answer | added | R.P. | timeline score: 14 | |
| Nov 3, 2012 at 16:18 | comment | added | Felipe Voloch | Yes, there are known p-adic analogues of Lindemann-Weierstrass, Gelfond-Schneider, Baker,... | |
| Nov 3, 2012 at 16:12 | history | asked | 36min | CC BY-SA 3.0 |