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A converse to Halász's theorem

Radziwiłł, Maksym (2011) A converse to Halász's theorem. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20180614-142647694

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Abstract

We show that the distribution of large values of an additive function on the integers, and the distribution of values of the additive function on the primes are related to each other via a Levy Process. As a consequence we obtain a converse to an old theorem of Halasz. Halasz proved that if f is an strongly additive function with f (p) ∈ {0, 1}, then f is Poisson distributed on the integers. We prove, conversely, that if f is Poisson distributed on the integers then for most primes p, f(p) = o(1) or f(p) = 1 + o(1).


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1109.0037arXivDiscussion Paper
Additional Information:The author is partially supported by a NSERC PGS-D award. This is part of author’s undergraduate thesis, written under the direction of Andrew Granville. The author would like to thank first and foremost Andrew Granville. There is too much to thank for, so it is simpler to note that this project would not surface without his constant support. Also, the author would like to thank Philippe Sosoe for proof-reading a substantial part of the old manuscript of this paper.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Classification Code:2010 Mathematics Subject Classification. Primary: 11N64, Secondary: 11N60, 11K65, 60F10
Record Number:CaltechAUTHORS:20180614-142647694
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180614-142647694
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87127
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Jun 2018 21:49
Last Modified:14 Jun 2018 21:49

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