不完整区间上整数及其逆的差

Differences of integers and their inverses over incomplete intervals

设实数λ,δ满足0<λ,δ1,n>2为整数.本文研究了不完整区间[1,[λn]]上整数与其模n逆的差.定义S(n,λ,δ)=#{a:1aλn,(a,n)=1,|a?a|<δn},本文给出了有关S(n,λ,δ)的一些渐近公式.

Let λ,δ be any real numbers with 0 λ,δ 1,and n 2 be an integer.We will study the differences of integers and their inverses modulo n over incomplete intervals [1,[λn]].Define S（n,λ,δ） = #{a：1 a λn,（a,n） = 1,｜a-a｜ δn}.Some asymptotic formulas of S（n,λ,δ） will be given.