Displaying similar documents to “The ℓ -rank of the real class group of cyclotomic fields”

The class number one problem for some non-abelian normal CM-fields of degree 24

F. Lemmermeyer, S. Louboutin, R. Okazaki (1999)

Journal de théorie des nombres de Bordeaux

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We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to 𝒜 4 , the alternating group of degree 4 and order 12 . There are two such fields with Galois group 𝒜 4 × 𝒞 2 (see Theorem 14) and at most one with Galois group SL 2 ( 𝔽 3 ) (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number 1 .

On the class numbers of real cyclotomic fields of conductor pq

Eleni Agathocleous (2014)

Acta Arithmetica

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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 methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields...

Artin's primitive root conjecture for quadratic fields

Hans Roskam (2002)

Journal de théorie des nombres de Bordeaux

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Fix an element α in a quadratic field K . Define S as the set of rational primes p , for which α has maximal order modulo p . Under the assumption of the generalized Riemann hypothesis, we show that S has a density. Moreover, we give necessary and sufficient conditions for the density of S to be positive.