TY - JOUR
T1 - Bases which admit exactly two expansions
AU - Cai, Yi
AU - Li, Wenxia
N1 - Publisher Copyright:
© 2023 University of Debrecen, Institute of Mathematics. All rights reserved.
PY - 2023
Y1 - 2023
N2 - Given a positive integer m, let Ωm = {0, 1, . . ., m}, and let B2(m) denote the set of bases q ∈ (1, m + 1] in which there exist numbers having precisely two q-expansions over the alphabet Ωm. Sidorov [23] firstly studied the set B2(1) and raised some questions. Komornik and Kong [15] further investigated the set B2(1) and partially answered Sidorov’s questions. In the present paper, we consider the set B2(m) for general positive integer m, and generalise the results obtained by Komornik and Kong.
AB - Given a positive integer m, let Ωm = {0, 1, . . ., m}, and let B2(m) denote the set of bases q ∈ (1, m + 1] in which there exist numbers having precisely two q-expansions over the alphabet Ωm. Sidorov [23] firstly studied the set B2(1) and raised some questions. Komornik and Kong [15] further investigated the set B2(1) and partially answered Sidorov’s questions. In the present paper, we consider the set B2(m) for general positive integer m, and generalise the results obtained by Komornik and Kong.
KW - generalized golden ratio
KW - q-expansion
KW - quasi-greedy q-expansion
KW - unique q-expansion
UR - https://www.scopus.com/pages/publications/85176404030
U2 - 10.5486/PMD.2023.9471
DO - 10.5486/PMD.2023.9471
M3 - 文章
AN - SCOPUS:85176404030
SN - 0033-3883
VL - 103
SP - 339
EP - 384
JO - Publicationes Mathematicae Debrecen
JF - Publicationes Mathematicae Debrecen
IS - 3-4
ER -