2015 Fiscal Year Final Research Report
On Weber's class number one problem
| Project/Area Number |
24540030
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Waseda University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 岩澤理論 / 類数 / Z_p-拡大 |
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| Outline of Final Research Achievements |
Let p be a prime number, B_p,∞ the cyclotomic Z_p-extension of the rational number field Q, B_p,n the n-th layer of B_p,∞/Q and h_p,n the class number of B_p,n. We obtained the following:
Let p be a prime number which is not congruent to 1 or -1 modulo 16. Then the p-part of the class number h_p,m,n of B_2,mB_p,n is bounded as n tends to infinity for the fixed m. We can see the result in [④].
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| Free Research Field |
整数論
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