论文标题
正方根的分数部分中的间隙
Gaps in the fractional parts of square roots
论文作者
论文摘要
第一个$ n $自然数的分数部分以渐近均匀的密度填充单位间隔。但是，围绕理性点的差距以渐近降低的速率$ n^{ - 1/2} $缩小，并使用Thomae（“爆米花”）功能缩小其宽度尺度。这种奇怪的联系是派生的，并与欧几里得果园中的阴影模式相关。还研究了较高自由基及其收敛速率的广义病例。
Fractional parts of the first $N$ natural numbers fill the unit interval with asymptotically uniform density. However, the gaps around rational points shrink at an asymptotically lower rate $N^{-1/2}$, and their widths scale with the Thomae ("popcorn") function. This curious connection is derived and related geometrically to shadow pattern in the Euclid's orchard. Generalized cases of higher radicals and their convergence rates, are also investigated.
