Length and denominators of egyptian fractions, III

Gérald Tenenbaum; Hisashi Yokota

doi:10.1016/0022-314X(90)90109-5

Length and denominators of egyptian fractions, III

Gérald Tenenbaum, Hisashi Yokota

Functional Control Systems

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

2 Citations (Scopus)

Abstract

We show that for large N every rational number a N ∈]0, 1[ has an egyptian fraction expansion a N = ∑ j=1 r 1 n_j where r ≤ (1 + o(1)) log N log₂N and n_r ≤ 4N log²N log₂N. This is essentially best possible.

Original language	English
Pages (from-to)	150-156
Number of pages	7
Journal	Journal of Number Theory
Volume	35
Issue number	2
DOIs	https://doi.org/10.1016/0022-314X(90)90109-5
Publication status	Published - 1990 Jun

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(90)90109-5

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title = "Length and denominators of egyptian fractions, III",

abstract = "We show that for large N every rational number a N ∈]0, 1[ has an egyptian fraction expansion a N = ∑ j=1 r 1 nj where r ≤ (1 + o(1)) log N log2N and nr ≤ 4N log2N log2N. This is essentially best possible.",

author = "G{\'e}rald Tenenbaum and Hisashi Yokota",

year = "1990",

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AU - Tenenbaum, Gérald

AU - Yokota, Hisashi

PY - 1990/6

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N2 - We show that for large N every rational number a N ∈]0, 1[ has an egyptian fraction expansion a N = ∑ j=1 r 1 nj where r ≤ (1 + o(1)) log N log2N and nr ≤ 4N log2N log2N. This is essentially best possible.

AB - We show that for large N every rational number a N ∈]0, 1[ has an egyptian fraction expansion a N = ∑ j=1 r 1 nj where r ≤ (1 + o(1)) log N log2N and nr ≤ 4N log2N log2N. This is essentially best possible.

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SP - 150

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Length and denominators of egyptian fractions, III

Abstract

ASJC Scopus subject areas

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