Class numbers in cyclotomic Zp-extensions
نویسندگان
چکیده
منابع مشابه
Cyclotomic Units and Class Groups in Zp-extensions of real abelian fields
For a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic Zp-extension of F . Assuming Greenberg’s conjecture about the vanishing of the λ-invariant of the extension, a map between these groups has been constructed by several authors, and shown to be an isomo...
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The class numbers h+l of the real cyclotomic fields Q(ζl + ζ −1 l ) are notoriously hard to compute. Indeed, the number h+l is not known for a single prime l ≥ 71. In this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζ −1 l ) for the primes l < 10, 000. It is quite likely that these subgroups are in fact equal to the class ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.11.008