A Caltech Library Service

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.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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 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.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Issue or Number:1
Classification Code:2010 Mathematics Subject Classification. Primary: 11M06, Secondary: 11M50.
Record Number:CaltechAUTHORS:20180618-152037832
Persistent URL:
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
Deposited By: George Porter
Deposited On:18 Jun 2018 22:36
Last Modified:03 Oct 2019 19:53

Repository Staff Only: item control page