Timeline for Does $P(\exp_p(a),\exp_p(b))=0$ imply $P=0$, where $\exp_p(\cdot)$ is $p$-adic exponential?
Current License: CC BY-SA 4.0
11 events
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| Apr 11, 2023 at 7:16 | comment | added | Achim Krause | If you have a linear dependency over $\mathbb{Q}$, you can clear denominators to get one with $\mathbb{Z}$ coefficients. I'm not sure how the answer you linked relates to what you want to do, you seem to jump back and forth between $\exp(a), \exp(b)$ being independent as elements, and $\exp(ta), \exp(tb)$ being independent as functions, which are different notions. | |
| Apr 11, 2023 at 6:57 | comment | added | MAS | @AchimKrause, I think in your answer $9^n \neq 17^m$ doesn't imply $a,b$ are linearly independent over $\mathbb Q$ because you considered $m,n$ to be integers only. Linear independency over $\mathbb Z$ may not imply linear independency over $\mathbb Q$. Can you see the comment of ACL below the accepted answer of this questin ? | |
| Apr 10, 2023 at 13:37 | vote | accept | MAS | ||
| Apr 10, 2023 at 13:24 | comment | added | Achim Krause | My counterexample (see my answer) still applies | |
| Apr 10, 2023 at 13:21 | comment | added | MAS | @AchimKrause, sorry, it was typo. see the edited question | |
| Apr 10, 2023 at 13:20 | history | edited | MAS | CC BY-SA 4.0 |
deleted 21 characters in body
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| Apr 10, 2023 at 12:35 | history | edited | Michael Hardy | CC BY-SA 4.0 |
proper use of \cdot
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| Apr 10, 2023 at 7:11 | answer | added | Achim Krause | timeline score: 3 | |
| Apr 10, 2023 at 7:03 | comment | added | Achim Krause | I don't understand how $P(\exp(a), \exp(b))=0$ implies $P(\exp(at), \exp(bt)) =0$ in your arguments. | |
| Apr 9, 2023 at 23:20 | history | edited | MAS | CC BY-SA 4.0 |
added 931 characters in body
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| Apr 9, 2023 at 22:53 | history | asked | MAS | CC BY-SA 4.0 |