Some Diophantine relations involving circular functions of rational angles
| dc.creator | Calogero, F. | |
| dc.creator | Perelomov, A. M. | |
| dc.date | 2001-12-10 | |
| dc.date.accessioned | 2026-07-07T04:28:48Z | |
| dc.date.available | 2026-07-07T04:28:48Z | |
| dc.description | The eigenvalues of the 3 off-diagonal matrices of rank $n$ with elements $1+i cot[(j-k)π/n], sin^{-2}[(j-k)π/n]$ and $sin^{-4}[(j-k)π/n], (j=1,2,...,n, k=1,2,...,n, j\neq k)$ are computed. The sums over $k$ from 1 to $n-1$ of $cot(kπ/n) sin(2skπ/n)$ and $sin^{-p}(kπ/n) cos(2skπ/n)$ are moreover computed for $s$ integer and $p=2$ and 4. The results are given by simple formulae in terms of integers. | |
| dc.description | 4 pages, an old paper (1979) posted for archival purposes | |
| dc.identifier | https://arxiv.org/abs/math-ph/0112014 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0112014 | |
| dc.identifier | Linear Algebra and Applications 25, 91-94 (1979) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56930 | |
| dc.subject | Mathematical Physics | |
| dc.title | Some Diophantine relations involving circular functions of rational angles | |
| dc.type | text |