發(fā)布時(shí)間：2019-05-13 18:18

【摘要】：整數(shù)及其逆的分布問題一直受到眾多數(shù)論學(xué)者的廣泛關(guān)注,人們對(duì)此進(jìn)行了深入研究,得到了豐富的成果.本文引入了不同整數(shù)冪模q剩余之差的分布問題,這是對(duì)整數(shù)及其逆的分布問題的一種推廣.文章主要利用初等數(shù)論、解析數(shù)論中的一些經(jīng)典的方法,并結(jié)合三角和的性質(zhì)及兩項(xiàng)指數(shù)和的估計(jì),研究了整數(shù)冪模q剩余之差的高次均值問題,得到了好的漸近公式.具體研究結(jié)果如下:令p為奇素?cái)?shù),α為正整數(shù),q= pα,m1,m2為不相等的正整數(shù)常數(shù),0δ,λ1,λ2≤1為實(shí)數(shù),k為非負(fù)的任意整數(shù).1.令a為滿足1 ≤ a ≤ q,(a,q)= 1的整數(shù),則存在唯一的整數(shù)b滿足1≤b ≤ g及其b三am1(mod q),記為(am1)q,即整數(shù)am1模q的最小正剩余.當(dāng)q[1/δ]時(shí),研究了整數(shù)冪模q剩余之差的高次均值分布,得到了漸近公式其中Σ'表示與q互素的整數(shù)之和,ε0為任意實(shí)數(shù),O所包含的常數(shù)與δ,m1,m2,k有關(guān);2.當(dāng)qmax{[1/λ1],[1/λ2}時(shí),研究了在不完整區(qū)間上Lehmer問題的推廣,漸近公式如下.其中O所包含的常數(shù)與λ1,λ2,m1,m2,κ有關(guān).
[Abstract]:The distribution of integers and their inverses has been widely concerned by many number theorists, which has been deeply studied and rich results have been obtained. In this paper, the distribution problem of the difference between different integer power modules Q is introduced, which is a generalization of the distribution problem of integers and their inverses. In this paper, by using the elementary number theory and some classical methods in the number theory, combined with the properties of the triangular sum and the estimation of the two exponential sums, the higher order mean value problem of the difference between the integers power module Q residue is studied, and a good asymptotic formula is obtained. The concrete results are as follows: let p be odd prime, 偽 be positive integer, Q = p 偽, M1, m2 be unequal positive integer constant, 0 未, 位 1, 位 2 鈮，

本文編號(hào)：2476087