On the local behavior of

Author:
Adolf Hildebrand

Journal:
Trans. Amer. Math. Soc. **297** (1986), 729-751

MSC:
Primary 11N25

MathSciNet review:
854096

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Abstract: denotes the number of positive integers and free of prime factors . In the range , can be well approximated by a "smooth" function, but for , this is no longer the case, since then the influence of irregularities in the distribution of primes becomes apparent. We show that behaves "locally" more regular by giving a sharp estimate for , valid in the range , .

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DOI:
https://doi.org/10.1090/S0002-9947-1986-0854096-0

Keywords:
Integers free of large primes factors,
asymptotic estimates

Article copyright:
© Copyright 1986
American Mathematical Society