Hexagonal Lattice Points on Circles
| dc.creator | Marmon, Oscar | |
| dc.date | 2005-08-11 | |
| dc.date.accessioned | 2026-07-07T05:22:18Z | |
| dc.date.available | 2026-07-07T05:22:18Z | |
| dc.description | We study the hexagonal lattice $\mathbb{Z}[ω]$, where $ω^6=1$. More specifically, we study the angular distribution of hexagonal lattice points on circles with a fixed radius. We prove that the angles are equidistributed on average, and suggest the possibility of constructing a consistent discrete velocity model (DVM) for the Boltzmann equation, using a hexagonal lattice. Equidistribution on average is expressed in terms of cancellation in exponential sums. We introduce Hecke L-functions and investigate their analytic properties in order to derive estimates on sums of Hecke characters. Using a version of the Halberstam-Richert inequality, these estimates then yield the desired results for the exponential sums. As a further measure of equidistribution, we give a bound for the discrepancy. | |
| dc.description | Master's Thesis. 53 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0508201 | |
| dc.identifier | http://arxiv.org/abs/math/0508201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76010 | |
| dc.subject | Number Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 11E25 (Primary) 82C40 (Secondary) | |
| dc.title | Hexagonal Lattice Points on Circles | |
| dc.type | text |