关于算术级数中Lehmer　D　H数的分布

On the Distribution of Lehmer D H Number in Arithmetical Progression

设ｑ＞２是一个奇数，对任意整数１≤ａ≤ｑ－１且（ａ，ｑ）＝１，存在唯一的整数１≤ａ≤ｑ－１，使得（ｍｏｄｑ），定义数ａ为Ｌｅｈｍｅｒ数，如果ａ和具有相反的奇偶性。研究算术级数中ＬｅｈｍｅｒＤＨ数的分布性质，并证明一个有趣的极限分布定理和渐近公式。

Let q>2 be an odd number,for each 1≤a≤q-1 with(a,q)=1,it is clear that there existsone and only one such that(mod q).Such number is called as a Lehmer D H num-ber if a and a are of opposite parity. The main purpose of this paper is to study the distribution prop-ertities of Lehmer D H number and give a sharper limiting distribution formula.