Timeline for Generalization of a determinant with Lucas numbers and totient functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2018 at 12:14 | comment | added | Max Alekseyev | Indeed. E.g., the formula in question directly follows from the one in my answer by setting $v_i=L_i^{\ell}$. | |
| Aug 26, 2018 at 0:39 | comment | added | Gjergji Zaimi | @darijgrinberg, yes that was mentioned in a previous question as well: mathoverflow.net/questions/262153/… . I think the second equality is the main part of the question. | |
| Aug 26, 2018 at 0:25 | comment | added | darij grinberg | Then, $\gcd\left(L_i, L_j\right)^{\ell} = \gcd\left(L_i^{\ell}, L_j^{\ell}\right)$, so your left hand side is the gcd-determinant for the $n$-tuple $\left(L_1^{\ell}, L_2^{\ell}, \ldots, L_n^{\ell}\right)$, which has a well-known formula (see, e.g., Lemma 7.1 in Chris Godsil, An Introduction to the Moebius Function, arXiv:1803.06664v1). | |
| Aug 26, 2018 at 0:17 | comment | added | T. Amdeberhan | Yes to the first. No to the second. | |
| Aug 25, 2018 at 23:29 | comment | added | darij grinberg | Do the $L_i$ form a gcd-sequence? That is, do we have $\gcd\left(L_i, L_j\right) = L_{\gcd\left(i,j\right)}$ ? And does your $\mathbb{N}$ contain $0$ ? | |
| Aug 25, 2018 at 23:28 | history | edited | darij grinberg | CC BY-SA 4.0 |
deleted 3 characters in body
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| Aug 25, 2018 at 23:20 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |