廣義Dedekind和與二項指數和的混合均值及一類丟番圖方程解的問題
發(fā)布時間：2019-06-21 02:00
【摘要】：數論是研究整數的各種性質的學科,具有“數學皇冠”稱號的數論是數學領域中最優(yōu)美的分支.作為高度抽象的學科,它的許多問題的研究和解決有著深遠的意義.其中關于數論中一些著名和式的均值分布問題一直是數論研究的核心內容.本文主要是利用初等方法和解析方法對廣義Dedekind和與二項指數和的混合均值及一類數論函數方程的解的問題進行了研究,具體研究成果包括以下幾方面的內容：1.通過廣義Dedekind和,二項指數和與Dirichlet L-函數問的關系,利用特征和估計及Dirichlet級數研究了廣義Dedekind和與二項指數和的混合均值,并給出了一些較強的漸近公式.形如：2.通過對指數Diophantine方程的研究,利用初等方法和Pell方程的最小解的特性,給出了當x,y是奇素數時,方程xz的正整數解的情況.
[Abstract]:Number theory is a subject that studies the various properties of integers, and the number theory with the title of "mathematical crown" is the most beautiful branch in the field of mathematics. As a highly abstract subject, the research and solution of many of its problems is of far-reaching significance. Among them, the mean distribution of some famous sums in number theory has always been the core content of number theory. In this paper, the mixed mean value of generalized Dedekind sum and binomial exponential sum and the solution of a class of number theory function equations are studied by using elementary method and analytical method. The concrete research results include the following aspects: 1. By using the relation between generalized Dedekind sum, binomial exponential sum and Dirichlet L-function, the mixed mean value of generalized Dedekind sum and binomial exponential sum is studied by using characteristic sum estimation and Dirichlet series, and some strong asymptotic formulas are given. In the form of: 2. By studying the exponential Diophantine equation, using the elementary method and the characteristics of the minimum solution of the Pell equation, the case of the positive integer solution of the equation xz is given when x, y is an odd prime.
【學位授予單位】：西北大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O156
本文編號：2503698
[Abstract]:Number theory is a subject that studies the various properties of integers, and the number theory with the title of "mathematical crown" is the most beautiful branch in the field of mathematics. As a highly abstract subject, the research and solution of many of its problems is of far-reaching significance. Among them, the mean distribution of some famous sums in number theory has always been the core content of number theory. In this paper, the mixed mean value of generalized Dedekind sum and binomial exponential sum and the solution of a class of number theory function equations are studied by using elementary method and analytical method. The concrete research results include the following aspects: 1. By using the relation between generalized Dedekind sum, binomial exponential sum and Dirichlet L-function, the mixed mean value of generalized Dedekind sum and binomial exponential sum is studied by using characteristic sum estimation and Dirichlet series, and some strong asymptotic formulas are given. In the form of: 2. By studying the exponential Diophantine equation, using the elementary method and the characteristics of the minimum solution of the Pell equation, the case of the positive integer solution of the equation xz is given when x, y is an odd prime.
【學位授予單位】：西北大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O156
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