Computation of Relative Class Numbers of Imaginary Abelian Number Fields
نویسنده
چکیده
Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.
منابع مشابه
Computation of class numbers of quadratic number fields
We explain how one can dispense with the numerical computation of approximations to the transcendental integral functions involved when computing class numbers of quadratic number fields. We therefore end up with a simpler and faster method for computing class numbers of quadratic number fields. We also explain how to end up with a simpler and faster method for computing relative class numbers ...
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In this abridged version of [Lou], we outline an efficient technique for computing relative class numbers of imaginary Abelian fields. It enables us to compute relative class numbers of imaginary cyclic fields of degrees 32 and conductors greater than 10, or of degrees 4 and conductors greater than 10. Our major innovation is a technique for computing numerically root numbers appearing in some ...
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Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...
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It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of 2-power degrees with class numbers equal to their genus class numbers.
متن کاملRelative class number of imaginary Abelian fields of prime conductor below 10000
In this paper we compute the relative class number of all imaginary Abelian fields of prime conductor below 10000. Our approach is based on a novel multiple evaluation technique, and, assuming the ERH, it has a running time of O(p2 log(p) log log(p)), where p is the conductor of the field.
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عنوان ژورنال:
- Experimental Mathematics
دوره 7 شماره
صفحات -
تاریخ انتشار 1998