Solution of small class number problems for cyclotomic fields
John Myron Masley (1976)
Compositio Mathematica
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Displaying similar documents to “On the class numbers of real cyclotomic fields of conductor pq”
Solution of small class number problems for cyclotomic fields
Class numbers of real cyclic number fields with small conductor
John Myron Masley (1978)
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Function fields with class number indivisible by a prime ℓ
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Class numbers of totally real fields and applications to the Weber class number problem
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The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application...
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Stéphane Louboutin (1999)
Colloquium Mathematicae
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We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.
On the ordinarity of the maximal real subfield of cyclotomic function fields
Daisuke Shiomi (2014)
Acta Arithmetica
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The aim of this paper is to clarify the ordinarity of cyclotomic function fields. In the previous work [J. Number Theory 133 (2013)], the author determined all monic irreducible polynomials m such that the maximal real subfield of the mth cyclotomic function field is ordinary. In this paper, we extend this result to the general case.