Polynomials in many variables
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-...
Polynomials of the form and pseudoprimes with respect to linear recurring sequences
Polynomials over solving an embedding problem
The fields defined by the polynomials constructed in E. Nart and the author in J. Number Theory 16, (1983), 6–13, Th. 2.1, with absolute Galois group the alternating group , can be embedded in any central extension of if and only if , or and is a sum of two squares. Consequently, for theses values of , every central extension of occurs as a Galois group over .
Polynomials that divide many trinomials
Polynomials whose values are powers.
Polynomials with height 1 and prescribed vanishing at 1.
Positive inverse Einheiten in komplexen kubischen Zahlkörpern
Positively ramified extensions of algebraic number fields.
Positiv-zerlegte p-Erweiterungen algebraischer Zahlkörper.
Potenzen von Galoisfeldern.
Potenzfreie Werte von Polynomen in algebraischen Zahlkörpern.
Potenzreste
Power integral bases in cubic relative extensions.
Power integral bases in orders of composite fields.
Power integral bases in the family of simplest quartic fields.
p-primary parts of unit traces and the p-adic regulator
p-Ranks of Class Groups in Zdp-Extensions.
Preuve de la conjecture de Langlands locale pour : travaux de Harris-Taylor et Henniart
Prime divisors of linear recurrences and Artin's primitive root conjecture for number fields
Let be a linear integer recurrent sequence of order , and define as the set of primes that divide at least one term of . We give a heuristic approach to the problem whether has a natural density, and prove that part of our heuristics is correct. Under the assumption of a generalization of Artin’s primitive root conjecture, we find that has positive lower density for “generic” sequences . Some numerical examples are included.