| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,500,000 (Direct Cost: ¥1,500,000)
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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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