Class number one criteria for real quadratic fields, I
نویسندگان
چکیده
منابع مشابه
Computation of Real Quadratic Fields with Class Number One
A rapid method for determining whether the real quadratic field Sí = S(\/D) has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of .W and then uses the Generalized Riemann Hypothesis to rapidly estimate L(l, x) to the accuracy needed for determining whether or not the class number of 3£ is one. The results of running this algor...
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For an even Dirichlet character , we obtain a formula for L(1;) in terms of a sum of Dirichlet L-series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coeecients. We then derive a class number formula for real quadratic number elds by taking L(s;) to be the quadratic L-series associated with these elds.
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a4 + 1 a5 + .. . will see that a less wasteful notation, say [ a0 , a1 , a2 , . . . ] , is needed to represent it. Anyone attempting to compute the truncations [ a0 , a1 , . . . , ah ] = ph/qh will be delighted to notice that the definition [ a0 , a1 , . . . , ah ] = a0 + 1/[ a1 , . . . , ah ] immediately implies by induction on h that there is a correspondence ( a0 1 1 0 ) ( a1 1 1 0 ) · · · (...
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We enumerate all one class genera of definite ternary quadratic forms over number fields. For this, we construct all Gorenstein orders of type number one in definite quaternion algebras over number fields. Finally, we list all definite quaternion orders of ideal class number one.
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In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire’s result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank ≥ 4, using a technique due to F. Hajir.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1987
ISSN: 0386-2194
DOI: 10.3792/pjaa.63.121