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On the distribution in short intervals of integers having no large prime factor
J. B. Friedlander and J. C. Lagarias, On the distribution in short intervals of integers having no large prime factor, Journal of Number Theory 25 (1987), 249–273. The selected text is the thirty-page author-hosted preprint, not the journal typesetting. The author's publication list, read 2026-10-15, identifies the publication and warns that its hosted preprints can omit editorial corrections and notes added in proof. No comparison with the journal version is recorded here.
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Scope
The introduction separates two questions for smooth integers in short intervals: whether every sufficiently late interval contains one, and whether it contains a positive proportion. Its functions and retain a quantifier over every smoothness exponent . Theorem 4 gives an explicit product construction for the existence question. A statement about an infimum of admissible exponents must not be read as a bound at its endpoint without checking the quantifiers.
Read status: claims checked. The introduction's definitions and Theorems 1–4 were read at statement depth in the selected preprint. The construction's proof and its translation to a block with a prescribed smoothness threshold have not been checked here.
Bears on. Problem 962: a uniform smooth-integer existence theorem is a potential input for excluding blocks whose every member has a prime factor exceeding the block length. The parameter match and endpoint requirements remain to be checked in any use.