Year: 2024
Type: article
Abstract: We prove that the set of Perron numbers that are not Parry numbers is dense in the interval $$(1,\infty )$$ ( 1 , ∞ ) and that the set of all Galois conjugates of such numbers is dense in the whole complex plane. While the Parry numbers themselves are known also to be dense in $$(1,\infty )$$ ( 1 , ∞ ) , their conjugates are known from work of Solomyak and others to be much more restricted: they are confined to a subset of the disc $$|z|<(1+\sqrt{5})/2$$ | z | < ( 1 + 5 ) / 2 . Our work is in response to a remark of Akiyama, drawing attention to our lack of knowledge about non-Parry Perron numbers and their conjugates.
Source: Research in Number Theory
Authors: Hachem Hichri, Chris Smyth
Institutions: University of Monastir, University of Edinburgh
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,490
OpenAlex ID: W4404394971