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Constructing hyperelliptic curves of genus 2 suitable for cryptography
 Math. Comp
, 2003
"... Abstract. In this article we show how to generalize the CMmethod for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation. 1. ..."
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Cited by 34 (2 self)
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Abstract. In this article we show how to generalize the CMmethod for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation. 1.
IDEAL CLASS GROUPS OF CYCLOTOMIC NUMBER FIELDS II
"... We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of pclass groups in cyclic ramified pextensions. ..."
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Cited by 9 (5 self)
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We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of pclass groups in cyclic ramified pextensions.
Computation of relative class numbers of CMfields by using Hecke Lfunctions
 Math. Comp
"... Abstract. We develop an efficient technique for computing values at s =1 of Hecke Lfunctions. We apply this technique to the computation of relative class numbers of nonabelian CMfields N which are abelian extensions of some totally real subfield L. We note that the smaller the degree of L the mo ..."
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Cited by 4 (2 self)
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Abstract. We develop an efficient technique for computing values at s =1 of Hecke Lfunctions. We apply this technique to the computation of relative class numbers of nonabelian CMfields N which are abelian extensions of some totally real subfield L. We note that the smaller the degree of L the more efficient our technique is. In particular, our technique is very efficient whenever instead of simply choosing L = N + (the maximal totally real subfield of N) we can choose L real quadratic. We finally give examples of computations of relative class numbers of several dihedral CMfields of large degrees and of several quaternion octic CMfields with large discriminants. 1.
Computation of relative class numbers of CMfields
 Math. Comp
, 1997
"... Abstract. It was well known that it is easy to compute relative class numbers of abelian CMfields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, SpringerVerlag, 1982). Here, we provide a technique fo ..."
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Cited by 3 (2 self)
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Abstract. It was well known that it is easy to compute relative class numbers of abelian CMfields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, SpringerVerlag, 1982). Here, we provide a technique for computing the relative class number of any CMfield. 1. Statement of the results Proposition 1. Let n ≥ 1 be an integer and α>1be real. Set Pn(x) = ∑n−1