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math.NT2017
On the number of integer polynomials with multiplicatively dependent roots
Arturas Dubickas, Min Sha
In this paper, we give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include s…
math.NT2017
On distances in lattices from algebraic number fields
Arturas Dubickas, Min Sha, Igor E. Shparlinski
In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introdu…