Let p be a prime number, K a finite abelian extension of Q containing p-th roots of unity and K n the n-th layer of the cyclotomic Z p -extension of K. Under some conditions we construct an element of K n from an ideal class of the maximal real subfield of K n . We determine whether its p-th root is contained by some Z p -extension of K n or not for each n, using the zero of p-adic L-function and the order of the ideal class group of the maximal real subfield of K m for sufficiently large m.
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Received: 13 February 1998 / Revised version: 30 September 1998
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Sumida, H. Initial layers of Zp-extensions and Greenberg's conjecture. manuscripta math. 98, 477–490 (1999). https://doi.org/10.1007/s002290050154
- Mathematics Subject Classification (1991):11R23