We introduce and study a family of functions we call the mock characters. These functions
satisfy a number of interesting properties, and of all completely multiplicative arithmetic …

Automatic sequences have many properties that other sequences (in particular, non-
uniformly morphic sequences) do not necessarily share. In this paper we survey a number of …

Automatic sequences are orthogonal to aperiodic multiplicative functions Page 1 Automatic
sequences are orthogonal to aperiodic multiplicative functions Mariusz Lemanczyk In 2010, P …

Generalised polynomials are maps constructed by applying the floor function, addition, and
multiplication to polynomials. Despite superficial similarity, generalised polynomials exhibit …

In this paper, we give a new proof and an extension of the following result of Bézivin. Let $
f:\mathbb {N}\to K $ be a multiplicative function taking values in a field $ K $ of characteristic …

We give a new proof of Fatou's theorem: if an algebraic function has a power series
expansion with bounded integer coefficients, then it must be a rational function. This result is …

A classical result due to Lagrange states that any natural number can be written as a sum of
four squares. Characterizations of integers that are a sum of two and three squares were …

Completely Multiplicative Automatic Functions Page 1 Integers 11 (2011), 731 – 738 DOI
10.1515/INTEG.2011.055 © de Gruyter 2011 Completely Multiplicative Automatic Functions …

We show that any automatic multiplicative sequence either coincides with a Dirichlet
character or is identically zero when restricted to integers not divisible by small primes. This …

A note on multiplicative automatic sequences, II - Klurman - 2020 - Bulletin of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …