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The distribution of r ‐tuples of square‐free numbers
Author(s) -
Tsang Kai-Man
Publication year - 1985
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300011049
Subject(s) - mathematics , sieve (category theory) , square free integer , square (algebra) , tuple , distribution (mathematics) , combinatorics , asymptotic formula , discrete mathematics , mathematical analysis , geometry
We use the Buchstab‐Rosser sieve to derive an asymptotic formula for the distribution of those integers n for which the r numbers n + l 1 , n + l 2 ,…, n + l r are all square‐free. Our error estimate sharpens a similar result of Hall and is uniform in both r and maxl 1≤i≤r |l i |.