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Published January 2013 | Submitted
Journal Article Open

Continuous lower bounds for moments of zeta and L-functions


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.

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.

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Submitted - 1202.1351.pdf


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August 19, 2023
October 18, 2023