Systems of equations depending on certain ideals
Tentative de description immobilière de quelques représentations intégrales de groupes finis (avec l'aide de Guy Rousseau)
The 2-divisibility of the class number of cyclotomic fields and the Stickelberger ideal.
The arithmetic of function fields
The calculation of large units in cyclic cubic fields.
The circular units and the Stickelberger ideal of a cyclotomic field revisited
The aim of this paper is a new construction of bases of the group of circular units and of the Stickelberger ideal for a family of abelian fields containing all cyclotomic fields, namely for any compositum of imaginary abelian fields, each ramified only at one prime. In contrast to the previous papers on this topic our approach consists in an explicit construction of Ennola relations. This gives an explicit description of the torsion parts of odd and even universal ordinary distributions, but it...
The construction of unramified abelian cubic extensions of a quadratic field
The digits of 1/p in connection with class number factors
The distribution of Kummer sums at prime arguments.
The exponent of class groups on congruence function fields
The Galois module of a twisted element in the -th cyclotomic field
The growth of Iwasawa invariants in a family
The Hasse norm principle in cyclotomic number fields.
The Hasse-Witt Matrix of a Formal Group.
The Image of the Atiyah-Bott Map.
The imaginary abelian number fields with class numbers equal to their genus class numbers
We know that there exist only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Such non-quadratic cyclic number fields are completely determined in [Lou2,4] and [CK]. In this paper we determine all non-cyclic abelian number fields with class numbers equal to their genus class numbers, thus the one class in each genus problem is solved, except for the imaginary quadratic number fields.
The -rank of the real class group of cyclotomic fields
The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems
The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s - conjecture for Galois extensions of number fields. It is certainly more difficult than the -localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number Conjecture for the case that and the degree of is an odd prime, with another small restriction on ramification. The very explicit calculations with cyclotomic units use trees and some classical combinatorics for bookkeeping. An important...
The Non-p-Part of the Class Number in a Cyclotomic ...p-Extension.
The refined p-adic abelian Stark conjecture in function fields.