二次函数域理想类数问题的一个注记

胡甦, 于宗文

数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 135-140.

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数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 135-140. DOI: 10.12386/A2010sxxb0018
论文

二次函数域理想类数问题的一个注记

    胡甦, 于宗文
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A Note on the Ideal Class Number Problem for Quadratic Function Fields

    Su HU, Zong Wen YU
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文章历史 +

摘要

应用 上的Pell方程这一初等方法重新证明一个已知的结果: 实二次函数域理想类数为1时, D只能为PQR, 其中P,Q,R中 的首一不可约多项式且 Q,R 次数为奇数.  

Abstract

Using Pell equations on , we give a new proof of the well-known fact that if the ideal class number of a real quadratic function field equals to 1, then D must be P or QR, where P,Q,R are monic and irreducible, and Q,R have odd degrees.  

关键词

二次函数域 / 理想类数 / Pell方程

Key words

quadratic function field / ideal class number / Pell equation

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导出引用
胡甦, 于宗文. 二次函数域理想类数问题的一个注记. 数学学报, 2010, 53(1): 135-140 https://doi.org/10.12386/A2010sxxb0018
Su HU, Zong Wen YU. A Note on the Ideal Class Number Problem for Quadratic Function Fields. Acta Mathematica Sinica, Chinese Series, 2010, 53(1): 135-140 https://doi.org/10.12386/A2010sxxb0018

参考文献



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