Lower bounds for moments of L-functions.
The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith [(2000) Commun. Math. Phys. 214, 57-89 and 91-110], 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.
Rudnick
Z
Z
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. rudnick@post.tau.ac.il
Soundararajan
K
K
D008433:Mathematics; D008962:Models, Theoretical