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CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA AND L-FUNCTIONS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  15 November 2012

Maksym Radziwiłł  and
Kannan Soundararajan
Maksym Radziwiłł
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, CA 94305-2125, U.S.A. (email: maksym@stanford.edu)
Kannan Soundararajan
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, CA 94305-2125, U.S.A. (email: ksound@math.stanford.edu)
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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.

MSC classification

Secondary: 11M06: $zeta (s)$ and $L(s, chi)$ 11M50: Relations with random matrices
Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013 , pp. 119 - 128
Copyright
Copyright © University College London 2012

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