On a conjecture of A. Schinzel and H. Zassenhaus
On a conjecture of D. H. Lehmer
On a question of Lehmer and the number of irreducible factors of a polynomial
On an approximation property of Pisot numbers II
Let be a complex number, be a positive rational integer and , where denotes the set of polynomials with rational integer coefficients of absolute value . We determine in this note the maximum of the quantities when runs through the interval . We also show that if is a non-real number of modulus , then is a complex Pisot number if and only if for all .
On families of Pisot -sequences
On gaps in Rényi -expansions of unity for an algebraic number
Let be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi -expansion of unity which controls the set of -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in are shown to exhibit a “gappiness” asymptotically bounded above by , where is the Mahler measure of . The proof of this result provides in a natural way a new classification of algebraic numbers with classes called Q...
On Garcia numbers.
On limits of PV k-tuples
On linear recurrence relations satisfied by Pisot sequences
On linear recurrence relations satisfied by Pisot sequences - Addenda and errata
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers and respectively, such that and are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On multiplicatively dependent linear numeration systems, and periodic points
Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.
On power series with only finitely many coefficients(mod 1): Solution of a problem of Pisot and Salem
On Roots of Polynomials with Positive Coefficients
On the Arithmetic of Special Values of L Functions.
On the arithmetic of two constructions of Salem numbers.
On the density of some sets of primes connected with cyclotomic polynomials
On the heights of totally -adic numbers
Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally -adic numbers and generalizations thereof. In this paper, we use potential theoretic techniques to generalize the upper bounds from their paper and, under the assumption of integrality, to improve slightly upon their bounds.
On the limit points of the fractional parts of powers of Pisot numbers
We consider the sequence of fractional parts , , where is a Pisot number and is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where and the unique limit point is zero, was earlier described by the author and Luca, independently.
On the topology of sums in powers of an algebraic number