Zeév Rudnick, Tel Aviv University
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,
there are now precise conjectures for their limiting values,
originally arrived via Random Matrix Theory. We develop a simple
method to establish lower bounds of the conjectured order of magnitude
for several such families of L-functions.
As an application we can show that the fluctuations of matrix elements
for the Laplacian on the modular domain are not Gaussian, contrary to
what is expected in the generic case for chaotic systems. (Joint work
with K. Soundararajan)