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Pretentiously detecting power cancellation

Published online by Cambridge University Press:  17 January 2013

JUNEHYUK JUNG  and
ROBERT J. LEMKE OLIVER
JUNEHYUK JUNG
Affiliation:
Princeton University, Department of Mathematics, Princeton, NJ 08544, U.S.A. e-mail: junehyuk@math.princeton.edu
ROBERT J. LEMKE OLIVER
Affiliation:
Emory University, Department of Mathematics and Computer Science, Atlanta, GA 30322, U.S.A. e-mail: rlemkeo@emory.edu
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Abstract

Granville and Soundararajan have recently introduced the notion of pretentiousness in the study of multiplicative functions of modulus bounded by 1, essentially the idea that two functions which are similar in a precise sense should exhibit similar behavior. It turns out, somewhat surprisingly, that this does not directly extend to detecting power cancellation - there are multiplicative functions which exhibit as much cancellation as possible in their partial sums that, modified slightly, give rise to functions which exhibit almost as little as possible. We develop two new notions of pretentiousness under which power cancellation can be detected, one of which applies to a much broader class of multiplicative functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 3 , May 2013 , pp. 481 - 498
Copyright
Copyright © Cambridge Philosophical Society 2013

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References

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