Class Number Computations of Real Abelian Number Fields
نویسندگان
چکیده
منابع مشابه
Efficient Computation of Class Numbers of Real Abelian Number Fields
Let {Km} be a parametrized family of real abelian number fields of known regulators, e.g. the simplest cubic fields associated with the Q-irreducible cubic polynomials Pm(x) = x −mx2 − (m+ 3)x− 1. We develop two methods for computing the class numbers of these Km’s. As a byproduct of our computation, we found 32 cyclotomic fields Q(ζp) of prime conductors p < 10 for which some prime q ≥ p divid...
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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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Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.
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Let {Km} be a parametrized family of simplest real cyclic cubic, quartic, quintic or sextic number fields of known regulators, e.g., the so-called simplest cubic and quartic fields associated with the polynomials Pm(x) = x3 − mx2 − (m + 3)x + 1 and Pm(x) = x4 − mx3 − 6x2 + mx + 1. We give explicit formulas for powers of the Gaussian sums attached to the characters associated with these simplest...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1982
ISSN: 0025-5718
DOI: 10.2307/2007347