Expansions in non-integer bases: Lower, middle and top orders
نویسندگان
چکیده
منابع مشابه
Expansions in Non-integer Bases: Lower, Middle and Top Orders
Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [4] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > (√5 + 1)/2, then there exist infinitely many x having a unique expansion [5]. In the present paper we begin the study of parameters q for which there...
متن کاملExpansions in Non-integer Bases: Lower, Middle and Top Order
Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑ ∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which th...
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Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which the...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2009
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2008.11.003