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
