# Hexagonal Lattice Points on Circles

Oscar Marmon
Göteborg : Chalmers tekniska högskola, 2005. 53 s. Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, ISSN 1652-9715, 2005.
[Examensarbete på avancerad nivå]

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.

Publikationen registrerades 2006-12-20. Den ändrades senast 2013-04-04

CPL ID: 24463

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