Generating function of the arithmetical function rd(n) and its relation to the Casimir energy
| dc.creator | Edery, Ariel | |
| dc.date | 2004-11-17 | |
| dc.date.accessioned | 2026-07-07T04:31:38Z | |
| dc.date.available | 2026-07-07T04:31:38Z | |
| dc.description | We obtain analytical expressions for the generating function $ξ_d(λ)$ of the sum of $d$-squares arithmetical function $r_d(n)$ where $λ$ is a free parameter. The original $d$-dimensional infinite sum is reduced to a formula containing a single finite sum over a convergent series. We compare the formulas to numerical computations and show that the percentage difference is negligible at small $λ$ for various values of $d$. $ξ_d(λ)$ divides naturally into two terms and we show that one term has a direct physical application to the $d$-dimensional Casimir energy of massless scalar fields in cubic cavities. | |
| dc.description | 18 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0411056 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0411056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57889 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Number Theory | |
| dc.title | Generating function of the arithmetical function rd(n) and its relation to the Casimir energy | |
| dc.type | text |