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math.NT2026
Mahler series with multiplicative coefficient sequences
Jason Bell, Daniel Smertnig
We prove that every Mahler series, over a field of characteristic , with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit…
math.NT2020★ 6 cited
A height gap theorem for coefficients of Mahler functions
Boris Adamczewski, Jason Bell, Daniel Smertnig
We study the asymptotic growth of coefficients of Mahler power series with algebraic coefficients, as measured by their logarithmic Weil height. We show that there are five differe…
math.NT2019★ 5 cited
Definite orders with locally free cancellation
Daniel Smertnig, John Voight
We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modul…