Algebraic function fields with equal class number
James Leitzel, Manohar Madan (1976)
Acta Arithmetica
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James Leitzel, Manohar Madan (1976)
Acta Arithmetica
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Ken Yamamura (1997)
Journal de théorie des nombres de Bordeaux
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We determine the structures of the Galois groups Gal of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis). For all such , is , the Hilbert class field of , the second Hilbert class field of , or the third Hilbert class field of . The use of Odlyzko’s discriminant bounds and information on the structure of class groups obtained by using the action of Galois groups on class groups is essential. We...
Ken Yamamura (2001)
Journal de théorie des nombres de Bordeaux
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In the previous paper [15], we determined the structure of the Galois groups of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors ) and give a table of . We update the table (under GRH). For 19 exceptional fields of them, we determine . In particular, for , we obtain , the fourth Hilbert class field of . This is the first example of a number...
Franz Lemmermeyer (1997)
Journal de théorie des nombres de Bordeaux
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Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields correspond to certain factorizations of its discriminant disc . In this paper we extend their results to unramified quaternion extensions of which are normal over , and show how to construct them explicitly.
Pieter Moree, Peter Stevenhagen (1997)
Acta Arithmetica
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Daniel Shanks, Peter Weinberger (1972)
Acta Arithmetica
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P. Elliott (1967)
Acta Arithmetica
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Stephen Cohen (1981)
Acta Arithmetica
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M. Kula (1981)
Acta Arithmetica
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Stéphane Louboutin (1997)
Acta Arithmetica
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