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Oscillatory properties of arithmetical functions. II. (English) Zbl 0631.10026
In the first paper in this series [ibid. 48, 173–185 (1986; Zbl 0613.10036)] the authors proved that a real-valued function \(f(x)\) has at least \(c(f) \log Y\) sign-changes in the interval \((0,Y]\) provided that the analytic continuation of its Mellin transform has all of its singularities of a certain form. The purpose of this paper is to generalize this result for a much wider class of functions. The theorem has immediate applications to the theory of distribution of prime numbers, the oscillatory properties of the difference \(\pi(x)-li(x)\), and of the similar difference for primes in an arithmetic progression.
Reviewer: W.E.Briggs

11N64 Other results on the distribution of values or the characterization of arithmetic functions
11N37 Asymptotic results on arithmetic functions
11N05 Distribution of primes
11N13 Primes in congruence classes
Full Text: DOI
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