论文标题
离散的分数积分，短弧线上的晶格点和Diophantine近似
Discrete fractional integrals, lattice points on short arcs, and diophantine approximation
论文作者
论文摘要
最近，在与E. sert的联合合作中，我们证明了沿二元二元形式的离散分数积分算子的尖锐界限结果。目前的工作通过扩展到双变量二次多项式来大大提高了这些结果的范围。我们通过在圆锥短弧线上建立与晶格点浓度的问题建立联系，从而通过统一的角度研究离散的分数积分和晶格点的浓度，从而通过筛分和双苯胺近似工具来研究离散的分数积分和晶格点的浓度，并证明这两个受试者对研究人员有利于研究人员，从而实现了这一目标。
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate quadratic polynomials. We achieve this in part by establishing connections to problems on concentration of lattice points on short arcs of conics, whence we study discrete fractional integrals and lattice point concentration from a unified perspective via tools of sieving and diophantine approximation, and prove theorems that are of interest to researchers in both subjects.
