Scharen quadratischer Zahlkörper mit gleichgebauten Einheiten
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de de degré premier impair
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de de degré premier impair
Si est une extension abélienne de de degré impair, l’étude du 2-groupe des classes (au sens ordinaire) de (et même celle de la parité du nombre de classes de ) est non triviale, et les algorithmes connus ne dépassent guère le cas .L’expression analytique de s’interprète à l’aide d’indices convenables de groupes d’unités cyclotomiques (Hasse et Leopoldt) ; ce dernier point de vue permet une caractérisation de la parité de , en fonction de l’existence d’unités cyclotomiques totalement...
Signatures of units and congruences (mod 4) in certain real quadratic fields. II.
Signatures of units and congruences (mod 4) in certain real quadratic fields.
Signatures of units and congruences (mod 4) in certain totally real fields.
Some generalizations of the Sₙ sequence of Shanks
Some more long continued fractions, I
Some new maps and ideals in classical Iwasawa theory with applications
We introduce a new ideal of the p-adic Galois group-ring associated to a real abelian field and a related ideal for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a -tower of abelian fields, and is linked by explicit reciprocity to a third ideal studied more generally in [D. Solomon, Acta Arith. 143 (2010)]. This leads to a new and unifying framework for the Iwasawa theory of such fields including a real analogue of Stickelberger’s Theorem,...
Some quartic number fields containing an imaginary quadratic subfield
Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.
Some remarks on factorization in algebraic number fields
Some Remarks on Leopoldt's Conjecture.
Some remarks on the decomposition of a rational prime in a Galois extension
Some results concerning certain periodic continued fractions
Some results concerning the nearest integer continued fraction expansion of ...D.
Some reults on fundamental units in cubic fields.
Some unsolved problems
Stark units and Kolyvagin's "Euler systems".
Stark's conjecture in multi-quadratic extensions, revisited
Stark’s conjectures connect special units in number fields with special values of -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.
Stickelberger ideal and signature of circular units.