On the regularized $L^4$-norm for Eisenstein series in the level aspect, Part II

TL;DR

This paper investigates the regularized fourth moment of newform Eisenstein series in the level aspect, providing conditional results and discussing truncated series, advancing understanding of their analytic properties.

Contribution

It offers a conditional analysis of the regularized fourth moment for newform Eisenstein series and explores the behavior of truncated series in the level aspect.

Findings

Conditional results for the regularized fourth moment

Discussion on the fourth moment of truncated Eisenstein series

Advancement in understanding Eisenstein series in the level aspect

Abstract

We obtain an conditional result for the regularized fourth moment of some newform Eisenstein series, using a recipe by Conrey, et al. We also discuss the fourth moment of truncated newform Eisenstein series.