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Computation of the Iwasawa invariants of certain real abelian fields

✍ Scribed by Hiroki Sumida-Takahashi

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 279 KB
Volume: 105
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2003.11.002

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✦ Synopsis

Let p be a prime number and k a finite extension of Q: It is conjectured that the Iwasawa invariants l p ðkÞ and m p ðkÞ vanish for all p and totally real number fields k: Some methods to verify the conjecture for each real abelian field k are known, in which cyclotomic units and a set of auxiliary prime numbers are used. We give an effective method, based on the previous one, to compute the exact value of the other Iwasawa invariant n p ðkÞ by using Gauss sums and another set of auxiliary prime numbers. As numerical examples, we compute the Iwasawa invariants associated to k ¼ Qð ffiffi ffi f p ; z p þ z À1 p Þ in the range 1of o200 and 5ppo10 000:

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