Sums of sets of continued fractions

T. W. Cusick; R. A. Lee

doi:10.1090/S0002-9939-1971-0282924-3

Sums of sets of continued fractions

T. W. Cusick
, R. A. Lee

Mathematics

SUNY Buffalo

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

For each integer k≧2, let S(k) denote the set of real numbers a such that O≦α≦K^-1 and α has a continued fraction containing no partial quotient less than k. It is proved that every number in the interval [0, 1 ] is representable as a sum of k elements of S(k).

Original language	English
Pages (from-to)	241-246
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	30
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1971-0282924-3
State	Published - Oct 1971

Keywords

Cantor sets
Continued fractions
Sums of sets

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10.1090/S0002-9939-1971-0282924-3

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title = "Sums of sets of continued fractions",

abstract = "For each integer k≧2, let S(k) denote the set of real numbers a such that O≦α≦K-1 and α has a continued fraction containing no partial quotient less than k. It is proved that every number in the interval [0, 1 ] is representable as a sum of k elements of S(k).",

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author = "Cusick, \{T. W.\} and Lee, \{R. A.\}",

year = "1971",

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doi = "10.1090/S0002-9939-1971-0282924-3",

language = "English",

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T1 - Sums of sets of continued fractions

AU - Cusick, T. W.

AU - Lee, R. A.

PY - 1971/10

Y1 - 1971/10

N2 - For each integer k≧2, let S(k) denote the set of real numbers a such that O≦α≦K-1 and α has a continued fraction containing no partial quotient less than k. It is proved that every number in the interval [0, 1 ] is representable as a sum of k elements of S(k).

AB - For each integer k≧2, let S(k) denote the set of real numbers a such that O≦α≦K-1 and α has a continued fraction containing no partial quotient less than k. It is proved that every number in the interval [0, 1 ] is representable as a sum of k elements of S(k).

KW - Cantor sets

KW - Continued fractions

KW - Sums of sets

UR - https://www.scopus.com/pages/publications/84968512879

U2 - 10.1090/S0002-9939-1971-0282924-3

DO - 10.1090/S0002-9939-1971-0282924-3

M3 - Article

AN - SCOPUS:84968512879

SN - 0002-9939

VL - 30

SP - 241

EP - 246

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

Sums of sets of continued fractions

Abstract

Keywords

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