數體及函數體上的密度問題;On Density Problems: the Case of Number Fields and the Case of Function Fields

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/49540

Title:	數體及函數體上的密度問題;On Density Problems: the Case of Number Fields and the Case of Function Fields
Authors:	陳燕美
Contributors:	數學系
Keywords:	數體;函數體;質數;密度;研究領域：數學類
Date:	2011-08-01
Issue Date:	2012-01-17 19:00:23 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	令K 是一個數體及P 是K 中所有質數所形成的集合。對任何一個P 的子集合M，令M(x) 代表集合M 中模小於或等於x 的元素個數，其中x 是一個(很大的) 實數。M 的自然密度被定義為分數 M(x)/P(x)的極限值(如果極限存在的話)，當x 趨於無窮大。在本計畫中，我們將探討在數體中各式各樣的密度問題然後嘗試建立在函數體的情形下的密度問題。 Let K be a number field and let P be the set of primes of K. For any subset M of P, denote by M(x) to be the number the subset of M consisting of primes of norm less than or equal to x, here x denotes a (however large) real number. The natural density of M is defined to be the limit (if the limit exists) of the fraction M(x)/P(x), as x goes to infinity. In this project, we will study various classical density problems in number field case and then try to establish their analogue in function field case. 研究期間：10008 ~ 10107
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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