1998 Fiscal Year Final Research Report Summary
Study of algebraic number fields related to Iwasawa invariants
| Project/Area Number |
09640065
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokai University |
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Principal Investigator |
HORIE Kuniaki Tokai University, School of Science, Associate Professor, 理学部, 助教授 (20201759)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Iwasawa lambda-invariant / Iwasawa mu-invariant / algebraic num-ber field / totally real field / CM-field / infinite extension / Iwasawa theory / number knot |
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| Research Abstract |
In Bulletin of the London Mathematical Society, 29 (1997), p. 367, the investigator corrected the error contained in the proof of a lemma of his earlier paper 'Two aspects of the relative lambda-invariant'. For each number field F, let F_<*, 3>, denote the basic Z_3-extension over F, lambda_3(F) the Iwasawa A-inveriant of F_<*, 3>, _<mu3> (F) the Iwasawa mu-invariant of F_<*, 3>/F.Given any number field kappa, let Q_- denote the infinite set of totally imaginary quadratic extensions over k, and Q_+ the infinite set of quadratic extensions over kappa in which every infinite place of kappa splits. The paper 'On quadratic extensions of number fields and Iwasawa invariants for basic Z_3-extensions' by the investigator and Iwao Kimura mainly proves that, if k is totally real, then a subset of [K * Q_- | lambda_3(K) = lambda_3(K), mu_3(K) = mu_3(k)} has an explicit positive density in Q_-. The paper also proves that a subsetof {L * Q_+ | lambda_3(L) = mu_3(L) = 0} has an explicit positive density in Q_+ if 3 does not divide the class number of k but is divided by only
one prime ideal of kappa.
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Research Products
(8 results)
