解析数论中一类和式的定量估计

Quantitative Estimates of a Class of Summation Formula in Analytic Number Theory

设实数α=aq+θq2满足(a,q)=1,q≥1,θ≤1.X≥1,Y≥1都是实数,研究了解析数论中∑x≤Xmin(XYx,12‖αx‖)的定量估计问题,得出了当α为有理数和实数时的定量估计结果.

Let real number α = a q ＋ θ q2 meet（a,q） = 1,q≥1,θ ≤1.X≥1,Y≥1 are real numbers.We study the problem of the quantitative estimate of ∑ x≤X min XY x,1（2 ‖αx‖）,and obtain the results when α is rational number and real number,respectirely.