| Ideal Class Groups and Subgroups of Real Quadratic Function Fields |
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| 作者姓名： | 张贤科 王鲲鹏 |
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| 作者单位： | ZHANG Xianke，WANG Kunpeng Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China; State Key Laboratory of Information Security，Graduate School at Beijing，University of Science and Technology of China，Beijing 100039，China |
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| 基金项目： | National Natural Science Foundation
of China! (No.197710 5 2 ) |
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| 摘 要： | ZhangandWashington1]studiedalgebraicquadraticnumberfieldsF=Q(d)andpresentedanecessaryandsufficientconditionfortheidealclassgroupH(F)ofanyrealfieldF=Q(d)tohaveacyclicsubgroupofordern.EightseriesofsuchfieldsFweregivenexplicitlybyutilizingthetheoryofcontinuedfractions.AllthesefieldsFareERD-typeorGERD-type,thatis,thediscriminatesdareoftheformd=N2 n,wheren|4Norn|2mN(m≥2)(ForthepropertiesofGERD-typefields,wereferthereaderstoRef.2]).Inthepresentnote,westudyalgebraicfunctionfieldsK,givean…
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Ideal Class Groups and Subgroups of Real Quadratic Function Fields |
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| ZHANG Xianke,WANG Kunpeng.Ideal Class Groups and Subgroups of Real Quadratic Function Fields[J].Tsinghua Science and Technology,2000,5(4). |
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| Authors: | ZHANG Xianke WANG Kunpeng |
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| Abstract: | In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(O K) of K in the series all have a factor n. |
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| Keywords: | algebraic function fields quadratic function field ideal class group continued fractiD |
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