Continuous lower bounds for moments of zeta and L-functions

Abstract

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.

9 pages

References in corpus (3)

• Lower bounds for moments of L-functions: symplectic and orthogonal examples
• The 4.36-th moment of the Riemann zeta-function
• Lower bounds for small fractional moments of Dirichlet $L$-functions

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• Moments of quadratic Dirichlet $L$-functions over Function Fields
• Rudnick and Soundararajan's Theorem for Function Fields
• Bounds for moments of Dirichlet $L$-functions to a fixed modulus
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• Hardy's function $Z(t)$ - results and problems
• Extreme central values of quadratic Dirichlet $L$-functions with prime conductors