4 papers
math.NT2025
A characterization of the distances between Pisot numbers generating the same number field
M. J. Bertin, T. Zaïmi
Let K be a real algebraic number field and let P be the set of Pisot numbers generating K. We show that the elements of P-P are the algebraic integers of K whose images under the a…
math.NT2024
On Salem numbers which are exceptional units II
Toufik Zaimi
We show that for any natural number satisfying and , and for any odd integer there are infinitely many Salem numb…
math.NT2023
On Salem numbers which are exceptional units
Toufik Zaimi
By extending a construction due to Gross and McMullen [2], we show that for any odd integer n and for any even integer d>n+2 there are infinitely many Salem numbers of degree d…
math.NT2021
On the trace of the integers of a number field
Francesco Battistoni, Toufik Zaïmi
Let denote the trace -module homomorphism defined on the ring of the integers of a number field We show that $Tr(\mathcal{O}_{L})\varsubset…