On Multiplicative Functions with Bounded Partial Sums

Details On Multiplicative Functions with Bounded Partial Sums On Multiplicative Functions with Bounded Partial Sums

2011-08-06

arxiv.org/abs/1108.1487v1

Mathematics

Number Theory

Scientific paper

Consider a multiplicative function f(n) taking values on the unit circle. Is it possible that the partial sums of this function are bounded? We show that if we weaken the notion of multiplicativity so that f(pn)=f(p)f(n) for all primes p in some finite set P, then the answer is yes. We also discuss a result of Bronstein that shows that functions modified from characters at a finite number of places.

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