## 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

### Keywords:

completely additive functions; set of quasi-uniqueness

Zbl 0153.06702
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