On the Cyclotomic Unit Group and the $p$-Ideal Class Group of a Real Abelian Number Field
نویسندگان
چکیده
منابع مشابه
Computation of the p-part of the ideal class group of certain real abelian fields
Under Greenberg’s conjecture, we give an efficient method to compute the p-part of the ideal class group of certain real abelian fields by using cyclotomic units, Gauss sums and prime numbers. As numerical examples, we compute the p-part of the ideal class group of the maximal real subfield of Q( √ −f, ζpn+1) in the range 1 < f < 200 and 5 ≤ p < 100000. In order to explain our method, we show a...
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1. Let g denote any odd prime and h = h(g) the class number of the cyclotomic field R(r), where r is the primitive gth root of unity, R the rational numbers. It is known that we can write: h = h1h2, where hi and h2 (both integers) are the so-called first and second factors of the class number; in fact h2 is the class number of the real field of degree 2 under R(r), namely the field R(D + D-). K...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1997
ISSN: 0387-3870
DOI: 10.3836/tjm/1270042113