A survey of results for Mahler measure of algebraic numbers, and one-variable polynomials
with integer coefficients is presented. Related results on the maximum modulus of the …

We prove that if f(x)=∑_k=0^n-1a_kx^k is a polynomial with no cyclotomic factors whose
coefficients satisfy a_k≡ 1 mod 2 for 0≤ k< n, then Mahler's measure of f satisfies …

A Pisot number is a real algebraic integer, all of whose conjugates lie strictly inside the open
unit disk; a Salem number is a real algebraic integer, all of whose conjugate roots are inside …

We describe an iterative method of constructing some favorable auxiliary polynomials used
to obtain lower bounds in some problems of algebraic number theory. With this method we …

The main result of this paper shows that every reciprocal Littlewood polynomial, one with {−
1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every …

The algorithms described in this paper were developed to investigate three problems
regarding polynomials with restricted coefficients:(i) determining whether there exist …

We show that the Mahler measure of every Borwein polynomial—a polynomial with
coefficients in {-1, 0, 1\} having non-zero constant term—can be expressed as a maximal …

Peter Borwein had wide-ranging mathematical interests, and was a pioneer in
computational and experimental investigations in many areas. We fondly recall some of his …

A polynomial f∈ ℂ [z] is unimodular if all its coefficients have unit modulus. Let U n denote
the set of unimodular polynomials of degree n− 1, and let U n∗ denote the subset of …

The idea behind the workshop was to bring together experts specializing in many different
fields: dynamical systems, K-theory, number theory, topology, analysis, to explore some of …