On the quartic character of quadratic units.
On the relation between units and Jacobi sums in Prime cyclotomic Fields.
On the representation of units by cyclotomic polynomials
On the Stark-Shintani units and the ideal class groups in the cyclotomic -extensions of class fields over real quadratic fields
On the Stickelberger Ideal and the Circular Units of an Abelian Field.
On the strongly ambiguous classes of some biquadratic number fields
We study the capitulation of -ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields , where and are different primes. For each of the three quadratic extensions inside the absolute genus field of , we determine a fundamental system of units and then compute the capitulation kernel of . The generators of the groups and are also determined from which we deduce that is smaller than the relative genus field . Then we prove that each...
On the structure of the group scheme
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1
On units and fundamental units.
On Washington group of circular units of some composita of quadratic fields
-adic Abelian Stark conjectures at
A -adic version of Stark’s Conjecture at is attributed to J.-P. Serre and stated (faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and work of Rubin) on the complex abelian case, we give a new approach to such a conjecture for real ray-class extensions of totally real number fields. We study the coherence of our -adic conjecture and then formulate some integral refinements, both alone and in combination with its complex analogue. A ‘Weak Combined Refined’ version...
Periodic expansions and units in quadratic and cubic number fields.
Periodic Jacobi-Perron expansions associated with a unit
We prove that, for any unit in a real number field of degree , there exits only a finite number of n-tuples in which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for . For we give an explicit algorithm to compute all these pairs.
Periodic points, multiplicities, and dynamical units.
Periods of sets of lengths: a quantitative result and an associated inverse problem
The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function...
Points périodiques des automorphismes affines.
Polynomials of Pellian Type and Continued Fractions
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex-...
Positive inverse Einheiten in komplexen kubischen Zahlkörpern
p-primary parts of unit traces and the p-adic regulator