Efficient computation of the Euler–Kronecker constants of prime cyclotomic fields
نویسندگان
چکیده
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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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On divisibility of the class number h+ of the real cyclotomic fields of prime degree l
In this paper, criteria of divisibility of the class number h+ of the real cyclotomic field Q(ζp +ζ−1 p ) of a prime conductor p and of a prime degree l by primes q the order modulo l of which is l−1 2 , are given. A corollary of these criteria is the possibility to make a computational proof that a given q does not divide h+ for any p (conductor) such that both p−1 2 , p−3 4 are primes. Note t...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2020
ISSN: 2522-0160,2363-9555
DOI: 10.1007/s40993-020-00213-1