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On sets characterizing number-theoretical functions. II: The set of “prime plus one” \(s\) is a set of quasi-uniqueness. (English) Zbl 0188.34302

By using the theorem of Bombieri it is proved that there exists a numerical constant \(K\) with the following property: if \(f(n)\) is a completely additive number-theoretic function such that \(f(p)=0\) for \(p\leq K\) and \(f(p+1)=0\) for all primes \(p\), then \(f(n)=0\), identically. the constant \(K\) in the theorem is non-effective.
For Part I, see Acta Arith. 13, 315–320 (1968; Zbl 0153.06702).
Reviewer: I. Kátai

MSC:

11N64 Other results on the distribution of values or the characterization of arithmetic functions

Citations:

Zbl 0153.06702
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