特徵值為2之平均值問題;On the Average Problems in Characteristic Two

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/57044

Title:	特徵值為2之平均值問題;On the Average Problems in Characteristic Two
Authors:	陳燕美
Contributors:	中央大學數學系
Keywords:	數學類;數體;函數體;理想類數;平均值;判斷式;原始判斷式 number fields;function fields;class numbers;average values;discriminants;fundamental discriminants
Date:	2009-09-01
Issue Date:	2012-10-01 15:10:23 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	有關二次數體的理想類數的平均值的研究可以追溯到Gauss 的時候。對於這個問題，他提出二個猜想，均已被證明。在1990 年代，Hoffstein 和 Rosen 考慮特徵值為奇質數的函數體上類推的問題。在最近幾年來，我們持續地探討特徵值為2 時的情況，對一般判斷式的平均值定理也得到不錯的成果。在本計畫中我們想要研究只考慮原始判斷式的平均值定理。 ; The study of the average value of class numbers of quadratic number fields can be dated back to Gauss. He proposed two conjectures on this problem, both have been proved. In 1990’s, Hoffstein and Rosen considered the analogue of function fields of odd characteristic. In recent years, we keep studying the arithmetic of quadratic function fields of characteristic two and obtain some nice results on averaging the class numbers of orders in quadratic function fields over all discrimanants. In this project, we would like to study the average value problem over fundamental discriminants only. ; 研究期間 9808 ~ 9907
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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