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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A differential delay equation arising from the sieve of Eratosthenes
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by A. Y. Cheer and D. A. Goldston PDF
Math. Comp. 55 (1990), 129-141 Request permission


The differential delay equation defined by $\omega (u) = 1/u$ for $1 \leq u \leq 2$ and $(u\omega (u))’ = \omega (u - 1)$ for $u \geq 2$ was introduced by Buchstab in connection with an asymptotic formula for the number of uncanceled terms in the sieve of Eratosthenes. Maier has recently used this result to show there is unexpected irregularity in the distribution of primes in short intervals. The function $\omega (u)$ is studied in this paper using numerical and analytical techniques. The results are applied to give some numerical constants in Maier’s theorem.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 129-141
  • MSC: Primary 11N35; Secondary 34K05
  • DOI:
  • MathSciNet review: 1023043