A prime sensitive Hankel determinant of Jacobi symbol enumerators
| dc.creator | Egecioglu, Omer | |
| dc.date | 2008-03-19 | |
| dc.date.accessioned | 2026-07-07T09:27:32Z | |
| dc.date.available | 2026-07-07T09:27:32Z | |
| dc.description | We show that the determinant of a Hankel matrix of odd dimension n whose entries are the enumerators of the Jacobi symbols which depend on the row and the column indices vanishes iff n is composite. If the dimension is a prime p, then the determinant evaluates to a polynomial of degree p-1 which is the product of a power of p and the generating polynomial of the partial sums of Legendre symbols. The sign of the determinant is determined by the quadratic character of -1 modulo p. The proof of the evaluation makes use of elementary properties of Legendre symbols, quadratic Gauss sums and orthogonality of trigonometric functions. | |
| dc.description | 13 pages, to appear in Annals of Combinatorics | |
| dc.identifier | https://arxiv.org/abs/0803.2834 | |
| dc.identifier | http://arxiv.org/abs/0803.2834 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157138 | |
| dc.subject | Combinatorics | |
| dc.subject | 11C20, 15A36, 11T24 | |
| dc.title | A prime sensitive Hankel determinant of Jacobi symbol enumerators | |
| dc.type | text |