Lower bounds for moments of L-functions

Abstract

The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith, there are now precise conjectures for their limiting values. We develop a simple method to establish lower bounds of the conjectured order of magnitude for several such families of L-functions. As an example we work out the case of the family of all Dirichlet L-functions to a prime modulus.

Cited by in corpus (32)

• The second moment of twisted modular L-functions
• Moments and distribution of central L-values of quadratic twists of elliptic curves
• Continuous lower bounds for moments of zeta and L-functions
• Sharp conditional bounds for moments of the Riemann zeta function
• Lower bounds for moments of L-functions: symplectic and orthogonal examples
• The second moment theory of families of L-functions
• Lower bounds for discrete negative moments of the Riemann zeta function
• Shifted moments of L functions and moments of theta functions
• Moments of quadratic twists of elliptic curve L-functions over function fields
• Moments of the Riemann zeta-function
• The sixth moment of automorphic $L$-functions
• A note on a conjecture of Gonek
• Negative values of the Riemann zeta function on the critical line
• Sharp upper bounds for moments of quadratic Dirichlet $L$-functions
• Simple zeros of modular L-functions
• Shifted moments of the Riemann zeta function
• The sixth power moment of Dirichlet L-functions
• Rudnick and Soundararajan's Theorem for Function Fields
• Moments of quadratic Dirichlet $L$-functions over Function Fields
• Lower bounds for moments of zeta prime rho
• The fourth moment of central values of quadratic Hecke $L$-functions in the Gaussian field
• The variance of arithmetic measures associated to closed geodesics on the modular surface
• Lower bounds for negative moments of ${\zeta }^{\prime }(\rho )$
• Bounds for moments of cubic and quartic Dirichlet $L$-functions
• On the correlation of shifted values of the Riemann zeta function
• Bounds for moments of Dirichlet $L$-functions to a fixed modulus
• Extreme values of zeta and L-functions
• Breaking the $\frac{1}{2}$-barrier for the twisted second moment of Dirichlet $L$-functions
• Lower bounds for moments of quadratic twisted self-dual $\text{GL}(3)$ central $L$-values
• A discrete mean value of the derivative of the Riemann zeta function
• The eighth moment of Dirichlet $L$-functions
• Lower bounds for moments of the derivative of the Riemann zeta function