1. OPTIMAL EXPANSIONS IN NON-INTEGER BASES.
- Author
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Dajani, Karma, De Vries, Martijn, Komornik, Vilmos, and Loreti, Paola
- Subjects
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INTEGERS , *MATHEMATICAL expansion , *NUMBER theory , *ALGEBRA , *MATHEMATICS - Abstract
For a given positive integer m, let A = {0, 1,… , m} and q ∈ (m,m+1). A sequence (ci) = c1c2 …. consisting of elements in A is called an expansion of x if ∑ ∞i=1 ciq-i = x. It is known that almost every x belonging to the interval [0,m/(q - 1)] has uncountably many expansions. In this paper we study the existence of expansions (di) of x satisfying the inequalities ∑n i=1 diq-i ⩾ ∑n i=1 ciq-i , n = 1, 2,… , for each expansion (ci) of x. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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