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
