圆上的晕格点
Hexagonal Lattice Points on Circles
摘要：
我们研究了六方晶格$\mathbb{Z}[ω]$，其中$ω^6=1$。更具体地说，我们研究了具有固定半径的圆上的六边形晶格点的角分布。我们证明，平均的角度是均匀分布的，并建议的可能性，构建一个一致的离散速度模型（DVM）的玻尔兹曼方程，使用一个六角形晶格。平均等分布用指数和的消去表示。我们引入Hecke L-函数并研究其解析性质，从而得到Hecke特征标和的估计。使用Halberstam-Richert不等式的一个版本，这些估计然后产生期望的结果的指数和。作为均匀分布的进一步度量，我们给出了差异的界。
英文摘要：
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.
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