| Project/Area Number |
23540019
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| 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
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | イデアル類群 / 類数 / 不定方程式 / 生成多項式 / 代数体 / 基本単数 / 連分数 |
|---|
| 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.
|
