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A note on the Liouville function in short intervals

Matomäki, Kaisa and Radziwiłł, Maksym (2015) A note on the Liouville function in short intervals. . (Submitted)

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In this note we give a short and self-contained proof that, for any δ > 0, ∑_(x≤n≤x+x^δ)λ(n) = o(x^δ) for almost all x ∈ [X,2X]. We also sketch a proof of a generalization of such a result to general real-valued multiplicative functions. Both results are special cases of results in our more involved and lengthy recent pre-print.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20180613-084923189
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87049
Deposited By: Tony Diaz
Deposited On:13 Jun 2018 16:15
Last Modified:03 Oct 2019 19:51

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