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On Multiplicative Functions with Bounded Partial Sums

Joseph Vandehey
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2012-0002


Consider a multiplicative function 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 for all primes p in some finite set P, then the answer is yes. We also discuss a result of Bronšteĭn that shows that functions modified from characters at a finite number of places must have unbounded partial sums.

Keywords: Multiplicative Function; Asymptotic Analysis; Character Sum; Erdős Discrepancy Problem

About the article

Received: 2011-07-19

Accepted: 2012-02-17

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 741–755, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0002.

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