Sums of sets of continued fractions
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- by T. W. Cusick and R. A. Lee PDF
- Proc. Amer. Math. Soc. 30 (1971), 241-246 Request permission
Abstract:
For each integer $k \geqq 2$, let $S(k)$ denote the set of real numbers $\alpha$ such that $0 \leqq \alpha \leqq {k^{ - 1}}$ and $\alpha$ 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 $S(k)$.References
- T. W. Cusick, Sums and products of continued fractions, Proc. Amer. Math. Soc. 27 (1971), 35–38. MR 269603, DOI 10.1090/S0002-9939-1971-0269603-3
- Marshall Hall Jr., On the sum and product of continued fractions, Ann. of Math. (2) 48 (1947), 966–993. MR 22568, DOI 10.2307/1969389
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 241-246
- MSC: Primary 10.31
- DOI: https://doi.org/10.1090/S0002-9939-1971-0282924-3
- MathSciNet review: 0282924