Hexagonal Lattice Points on Circles

Examensarbete för masterexamen

Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12380/24463
 Type: Examensarbete för masterexamenMaster Thesis Title: Hexagonal Lattice Points on Circles Authors: Marmon, Oscar Abstract: We study the hexagonal lattice $\mathbb{Z}[\omega]$, where $\omega^6=1$. 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 possibilty 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. Keywords: Matematik;Mathematics Issue Date: 2005 Publisher: Chalmers tekniska högskola / Institutionen för matematiska vetenskaperChalmers University of Technology / Department of Mathematical Sciences Series/Report no.: Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University URI: https://hdl.handle.net/20.500.12380/24463 Collection: Examensarbeten för masterexamen // Master Theses