Abstract: In 2008, Akiyama, Frougny and Sakarovitch introduced an algorithm to expand real numbers in a rational base a/b using the digits
{0,...,|a|-1}, which differs from the greedy algorithm and gives rise to an interesting language. In this talk, we will characterize these
expansions in terms of p-adic numbers, and we will present a generalization to complex bases. Given an algebraic number alpha (in
principle, we assume it is a Gaussian rational with modulus greater than one), we introduce an algorithm to find an expansion of a given complex
number in this base, using a suitable set of digits. We will relate these expansions to a family of fractals, and characterize them in terms
of p-adic completions with respect to Gaussian primes.
Digit expansions in rational and algebraic bases
30.10.2025 15:15 - 17:30
Organiser:
H. Bruin, R. Zweimüller
Location: