Continuous lower bounds for moments of zeta and L-functions

Details Continuous lower bounds for moments of zeta and L-functions Continuous lower bounds for moments of zeta and L-functions

2012-02-07

arxiv.org/abs/1202.1351v1

Mathematics

Number Theory

9 pages

Scientific paper

We obtain lower bounds of the correct order of magnitude for the 2k-th 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.

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