14 citations · 68 across the 34 of their papers we have counts for
4 papers · 2 filters
Algebraic independence of Mahler functions via radial asymptotics
Richard P. Brent, Michael Coons, Wadim Zudilin
We present a new method for algebraic independence results in the context of Mahler's method. In particular, our method uses the asymptotic behaviour of a Mahler function as…
Growth degree classification for finitely generated semigroups of integer matrices
Jason P. Bell, Michael Coons, Kevin G. Hare
Let be a finite set of matrices with integer entries and let be the maximum norm of a product of elements of . In this…
The minimal growth of a -regular sequence
Jason P. Bell, Michael Coons, Kevin G. Hare
We determine a lower gap property for the growth of an unbounded \(\mathbb{Z}\)-valued \(k\)-regular sequence. In particular, if \(f:\mathbb{N}\to\mathbb{Z}\) is an unbounded \(k\)…
Towards the (ir)rationality of values of Dirichlet series
Michael Coons, Daniel Sutherland
We show that if is a nondegenerate ordinary Dirichlet series with nonnegative coefficients and is a rational number for all large enough positive integers , then t…