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Continuous lower bounds for moments of zeta and L-functions

Radziwiłł, Maksym and Soundararajan, Kannan (2013) Continuous lower bounds for moments of zeta and L-functions. Mathematika, 59 (1). pp. 119-128. ISSN 0025-5793. https://resolver.caltech.edu/CaltechAUTHORS:20180618-152037832

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Abstract

We obtain lower bounds of the correct order of magnitude for the 2kth moment of the Riemann zeta function for all k≥1. Previously such lower bounds were known only for rational values of k, with the bounds depending on the height of the rational number k. Our new bounds are continuous in k, and thus extend also to the case when k is irrational. The method is a refinement of an approach of Rudnick and Soundararajan, and applies also to moments of L-functions in families.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1112/S0025579312001088PublisherArticle
http://arxiv.org/abs/1202.1351arXivDiscussion Paper
Additional Information:© University College London 2012. In memoriam Professor K. Ramachandra (1933-2011). The first author is partially supported by a NSERC PGS-D award. The second author is partially supported by NSF grant DMS-1001068.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
NSFDMS-1001068
Issue or Number:1
Classification Code:2010 Mathematics Subject Classification. Primary: 11M06, Secondary: 11M50.
Record Number:CaltechAUTHORS:20180618-152037832
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180618-152037832
Official Citation:Radziwiłł, M., & Soundararajan, K. (2013). CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA AND L-FUNCTIONS. Mathematika, 59(1), 119-128. doi:10.1112/S0025579312001088
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87205
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:18 Jun 2018 22:36
Last Modified:03 Oct 2019 19:53

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