• Corpus ID: 16198745

On the Computation of the Class Numbers of Real

@inproceedings{Hakkarainen2007OnTC,
  title={On the Computation of the Class Numbers of Real},
  author={Tuomas Hakkarainen},
  year={2007}
}
Acknowledgements I wish to express my sincere gratitude to my supervisor, Professor Tauno Metsänkylä, for his continuous support during this work. Without his excellent guidance and broad knowledge, this thesis would not have been possible. I am very grateful to Professors Radan Kučera and Horst-Günter Zimmer for reviewing the thesis manuscript and for their invaluable suggestions and remarks. I thank the Department of Mathematics and Turku Centre of Computer Science TUCS for providing… 

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References

SHOWING 1-10 OF 44 REFERENCES
Heuristics for class numbers of prime-power real cyclotomic fields
Abstract. Let h(`) denote the class number of the maximal totally real subfield Q(cos(2π/`n)) of the field of `n-th roots of unity. The goal of this paper is to show that (speculative extensions of)
Class numbers of real cyclotomic fields of prime conductor
TLDR
This paper presents a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζl-1) for the primes l > 10,000 and argues that it is quite likely that these subgroups are in fact equal to theclass groups themselves, but there is at present no hope of proving this rigorously.
Class number computations of real abelian number fields
In this paper we describe the calculation of the class numbers of most real abelian number fields of conductor ? 200. The technique is due to J. M. Masley and makes use of discriminant bounds of A.
P-class Groups of Certain Extensions of Degree P
TLDR
A heuristic principle is formulated predicting the distribution of the p-class groups as Galois modules, which is analogous to the Cohen-Lenstra heuristics concerning the prime-to-p-part of the class group, although in this case the number of primes that ramify in the extensions considered is fixed.
Critère effectif de puissancep-ième dans un corps de nombres galoisien
Resume Lete≠0 be an integer of a Galois extensionK/ Q (of degreenand Galois groupG), and letpbe a prime number. Let (e′σ)σ∈Gbe a family of approximations (in C ) of suitablepth rootseσof theσ(e),σ∈G.
The prime factors of Wendt’s binomial circulant determinant
Wendt’s binomial circulant determinant, W„, is the determinant of an m by m circulant matrix of integers, with (i, j)th entry (i, ™.i) whenever 2 divides m but 3 does not. We explain how we found the
Class numbers of real cyclic number fields with small conductor
© Foundation Compositio Mathematica, 1978, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions
Quintic polynomials and real cyclotomic fields with large class numbers
We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several
A condition for divisibility of the class number of real pth cyclotomic field by an odd prime distinct from p
Let p > 3 be an odd prime. Let ~" = ~'p = cos(2zr/p) + i s in(2rr/p) be a primitive pth root of unity. Let Q(~-p)+ denote the maximal real subfield of the pth cyclotomic field Q(~'p), i.e., Q(~'p)+ =
Calculation of the class numbers and fundamental units of abelian extensions over imaginary quadratic fields from approximate values of elliptic units
0.1. Any number field we consider is a finite extension of the rational number field $Q$ in the complex number field $C$ . Let $L/F$ be an abelian extension of number fields. For $L$ , denote its
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