特殊集合上特征和的估计

发布时间：2019-03-07 17:07

【摘要】：特征和作为解析数论的重要研究对象之一,在解析数论的发展中起着非常重要的作用,针对它的研究广泛而丰富.特征和估计在解析数论中占有重要地位,它与许多著名数论问题有着非常密切的关系,对各种类型的特征和的上界估计一直倍受学者们青睐.长久以来,许多学者致力于特征和上界估计的改进和优化.在不同集合上探究特征和的估计,对揭示特征和的值分布规律有重要作用.本文利用Dirichlet特征和的性质和与之相关的算术函数的性质,结合数论研究中的一些初等方法及相关文献中提及的方法,研究了在一些特殊数集上特征和的值分布问题,给出了较强的上界估计.主要结论如下:1.设整数l≥ 2,q ≥ 3是无平方因子的整数,X是模q的非主特征,对满足3 ≤ H ≤ q的整数H,定义集合有如下估计其中ω(q)表示q的不同素因子的个数.2.设素数p ≥ 3,整数m ≥ 2,X是模q的奇特征,定义集合有如下估计3.设奇数q ≥ 3,x是模q的非主特征,对于满足3 ≤ H ≤ q的整数H,定义集合F(H,q)= {a ∈ Z|(a,q)= 1,1 ≤ a,b ≤ q,ab = 1(mod q),|a-b| ≤ H,2(?)(a+b)},有如下结果
[Abstract]:As one of the important research objects of the number theory, it plays a very important role in the development of the number theory, and is rich in its research. The characteristic and the estimation have an important position in the number theory, and it has a very close relation with many famous theory problems, and it has always been the favor of the scholars for all kinds of characteristics and the upper bound of the upper bound. For a long time, many scholars are committed to the improvement and optimization of the estimation of the characteristics and the upper bound. It is important to explore the characteristics and the estimation of the characteristics and the distribution of the values in different sets. In this paper, using the nature of the Dirichlet feature and the property of the arithmetic function associated with it, some elementary methods and the methods mentioned in the related literature are used to study the characteristic and the value distribution problem in some special data sets, and a strong upper bound estimation is given. The main conclusions are as follows:1. Let the integer l-2, q-3 be an integer without a square factor, X is the non-main feature of the mode q, and the set has the following estimation of the number of different prime factors in which the integer (q) represents q. Let's set the prime number p-3, the integer m-2, and X is the odd feature of the mode q, and the definition set has the following estimate 3. An odd number of q = 3, x is the non-main feature of the mode q. For an integer H that satisfies the 3-H-value q, the set F (H, q) = {a} Z | (a, q) = 1,1, a, b, q, ab = 1 (mod q), | a-b | {H,2 (?) (a + b)} is defined as follows
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O156.4

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