Class number of real Abelian 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...
متن کاملOn the computation of class numbers of real abelian fields
In this paper we give a procedure to search for prime divisors of class numbers of real abelian fields and present a table of odd primes < 10000 not dividing the degree that divide the class numbers of fields of conductor ≤ 2000. Cohen–Lenstra heuristics allow us to conjecture that no larger prime divisors should exist. Previous computations have been largely limited to prime power conductors.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.09.027