Solution of small class number problems for cyclotomic fields
John Myron Masley (1976)
Compositio Mathematica
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Displaying similar documents to “Class numbers of real cyclic number fields with small conductor”
Solution of small class number problems for cyclotomic fields
The -rank of the real class group of cyclotomic fields
Gary Cornell, Michael I. Rosen (1984)
Compositio Mathematica
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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...
Kronecker-Weber via Stickelberger
Franz Lemmermeyer (2005)
Journal de Théorie des Nombres de Bordeaux
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In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.
The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
Stéphane Louboutin (1998)
Colloquium Mathematicae
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It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.
Annihilators of the class group of a compositum of quadratic fields
Jan Herman (2013)
Archivum Mathematicum
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This paper is devoted to a construction of new annihilators of the ideal class group of a tamely ramified compositum of quadratic fields. These annihilators are produced by a modified Rubin’s machinery. The aim of this modification is to give a stronger annihilation statement for this specific type of fields.
The class number one problem for some non-abelian normal CM-fields of degree
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 , the alternating group of degree and order . There are two such fields with Galois group (see Theorem 14) and at most one with Galois group SL (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number .
A survey of computational class field theory
Henri Cohen (1999)
Journal de théorie des nombres de Bordeaux
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We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.