The $L^4$-norm problems for newform Eisenstein series

Let $E$ be an Eisenstein series of primitive nebentypus mod $N$. We reduce
the regularized $L^4$-norm of $E$ to an average of automorphic $L$-functions, for all large $N$. The result is the level aspect analogue of the work by Djanković and Khan for classical Eisenstein series. With this reduction, we can see two new problems: how to estimate this sum, and what should be the Random Wave Conjecture for the fourth moment of the truncated newform Eisenstein series. I will also show the progress on solving the two problems.

Zoom Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).