On Iwasawa $\lambda_3$-invariants of cyclic cubic fields of prime conductor
نویسندگان
چکیده
منابع مشابه
On Iwasawa Λ3-invariants of Cyclic Cubic Fields of Prime Conductor
For certain cyclic cubic fields k, we verified that Iwasawa invariants λ3(k) vanished by calculating units of abelian number field of degree 27. Our method is based on the explicit representation of a system of cyclotomic units of those fields.
متن کاملOn Iwasawa lambda3-invariants of cyclic cubic fields of prime conductor
For certain cyclic cubic fields k, we verified that Iwasawa invariants λ3(k) vanished by calculating units of abelian number field of degree 27. Our method is based on the explicit representation of a system of cyclotomic units of those fields.
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If p is an odd prime that does not divide the class number of the imaginary quadratic field k , and the cyclotomic Z -extension of k has A-invariant less than or equal to two, we prove that every totally ramified Z extension of k has //-invariant equal to zero and A-invariant less than or equal to two. Combined with a result of Bloom and Gerth, this has the consequence that ß = 0 for every Z -e...
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Let p be a prime number and k a finite extension of Q. It is conjectured that Iwasawa invariants λp(k) and μp(k) vanish for all p and totally real number fields k. Using cyclotomic units and Gauss sums, we give an effective method for computing the other Iwasawa invariants νp(k) of certain real abelian fields. As numerical examples, we compute Iwasawa invariants associated to k = Q( √ f, ζp + ζ...
متن کاملClass numbers of real cyclotomic fields of prime conductor
The class numbers h+l of the real cyclotomic fields Q(ζl + ζ −1 l ) are notoriously hard to compute. Indeed, the number h+l is not known for a single prime l ≥ 71. In this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζ −1 l ) for the primes l < 10, 000. It is quite likely that these subgroups are in fact equal to the class ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2000
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-00-01284-9