2013 Fiscal Year Final Research Report
Study of ideal class groups of algebraic number fields by using Diophantine equations and generic polynomials
Project/Area Number |
23540019
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Aichi University of Education |
Principal Investigator |
KISHI Yasuhiro 愛知教育大学, 教育学部, 准教授 (60380375)
|
Project Period (FY) |
2011 – 2013
|
Keywords | イデアル類群 / 類数 / 不定方程式 / 生成多項式 / 代数体 |
Research Abstract |
In this research, we investigated Diophantine equations and generic polynomials in order to construct algebraic number fields whose ideal class groups are not cyclic. As a result, for a prime number p which is congruent to 3 modulo 4, we gave explicitly an infinite family of imaginary cyclic fields of degree p-1 whose ideal class groups have p-rank at least 2. We also gave a refinement of Spiegelung relation for p=3, and got a new infinite family of imaginary quadratic fields whose ideal class groups have 3-rank at least 2.
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