We prove that if $ P (X)\in\mathbb {Z}[X] $ is an integer polynomial of degree $ n $ and
having $ P (0)= 1$, then either $ P (X) $ is a product of cyclotomic polynomials, or else at …

We characterize group representations that factor through monomial representations,
respectively, block-triangular representations with monomial diagonal blocks, by arithmetic …

In previous work, the first author, Ghioca, and the third author introduced a broad dynamical
framework giving rise to many classical sequences from number theory and algebraic …

We prove a general criterion for an irrational power series $ f (z)=\sum _ {n= 0}^{\infty} a_nz^
n $ with coefficients in a number field $ K $ to admit the unit circle as a natural boundary. As …

We consider D-finite power series f (z)=∑ n≥ 0 anzn with coefficients in a number field K.
We show that there is a dichotomy governing the behaviour of h (an) as a function of n …

We prove a uniform version of the Dynamical Mordell–Lang Conjecture for étale maps; also,
we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary …

We show that in a parametric family of linear recurrence sequences with the coefficients and
characteristic roots,, given by rational functions over some number field, for all but a set of …

In 1971, Ruzsa conjectured that if f: N→ Z with f (n+ k)≡ f (n) mod k for every n, k∈ N and f
(n)= O (θ n) with θ< e then f is a polynomial. In this paper, we investigate the analogous …

Let K be an algebraically closed field of characteristic zero, let G be a finitely generated
subgroup of the multiplicative group of K, and let X be a quasiprojective variety defined over …

We prove a result that can be seen as an analogue of the Pólya–Carlson theorem for
multivariate D-finite power series with coefficients in Q¯. In the special case that the …