On the Ideal Class Groups of Real Abelian Number Fields

Thaine, Francisco

doi:10.2307/1971460

Cited by 62 publications

(32 citation statements)

References 3 publications

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“…The image of these maps in Aoki's paper, when applied on cyclotomic units give higher annihilators for the l-part of h + . These ideas are based on the work of Thaine [28], as well as on the work of V.…”

Section: Introductionmentioning

confidence: 99%

On the class numbers of real cyclotomic fields of conductor pq

Agathocleous

2014

Acta Arith.

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The class numbers h + of the real cyclotomic fields are very hard to compute.Methods based on discriminant bounds become useless as the conductor of the field grows and that is why other methods have been developed, which approach the problem from different angles. In this thesis we extend a method of Schoof that was designed for real cyclotomic fields of prime conductor to real cyclotomic fields of conductor equal to the product of two distinct odd primes. Our method calculates the index of a specific group of cyclotomic units in the full group of units of the field.This index has h + as a factor. We then remove from the index the extra factor that does not come from h + and so we have the order of h + . We apply our method to real cyclotomic fields of conductor < 2000 and we test the divisibility of h + by all primes < 10000. Finally, we calculate the full order of the l-part of h + for all odd primes l < 10000.

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Section: Introductionmentioning

confidence: 99%

On the class numbers of real cyclotomic fields of conductor pq

Agathocleous

2014

Acta Arith.

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“…In a recent paper [9], Francisco Thaine showed how to use cyclotomic units to construct annihilators of ideal class groups of real abelian extensions of Q. His method is similar to an idea of Kummer [5] which had previously been overlooked.…”

Section: W Introductionmentioning

confidence: 99%

Global units and ideal class groups

Rubin

1987

Invent Math

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“…We can prove that Char(C + ) divides Char(U/ z) by the method of Euler system (Kolyvagin's idea [25]; Thaine [42] had partially a similar idea) using the Euler system property of cyclotomic units (2.5.2 (b)). The method here is simply speaking as in 2.5.4 below.…”

Section: 53mentioning

confidence: 99%