منابع مشابه
Computation of Iwasawa ν-invariants of certain real abelian fields
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 کاملEfficient Computation of Class Numbers of Real Abelian Number Fields
Let {Km} be a parametrized family of real abelian number fields of known regulators, e.g. the simplest cubic fields associated with the Q-irreducible cubic polynomials Pm(x) = x −mx2 − (m+ 3)x− 1. We develop two methods for computing the class numbers of these Km’s. As a byproduct of our computation, we found 32 cyclotomic fields Q(ζp) of prime conductors p < 10 for which some prime q ≥ p divid...
متن کاملThe Iwasawa Invariants and the Higher K-Groups Associated to Real Quadratic Fields
First, let us look back over the case of χ = χ the trivial character. For k = 1, Bk,χ0 is the kth Bernoulli number Bk, and B1,χ0 = B1 + 1 = 1/2. A pair of integers (p, k) is said to be an irregular pair if p is a prime, k is an even integer satisfying 2 ≤ k ≤ p−3, and p divides the numerator of Bk = Bk,χ0 . Irregular pairs have been computed by Kummer, Vandiver, D.H. Lehmer, E. Lehmer, Selfridg...
متن کاملOn Small Iwasawa Invariants and Imaginary Quadratic Fields
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...
متن کاملDuality Theorems in the Multivariable Iwasawa Theory of Number Fields
1. Introduction. Let K be a number field, let p be an odd prime, and let K ∞ /K be an extension containing all p-power roots of unity whose Galois group Γ is isomorphic to Z
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1996
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0023