Eisenstein series of even weight $k \geq 2$ and integral binary quadratic forms

TL;DR

This paper proves a conjecture regarding the analytic continuation of hyperbolic Eisenstein series of weight 2 for the full modular group, advancing understanding in the theory of automorphic forms.

Contribution

It establishes the analytic continuation of hyperbolic Eisenstein series of weight 2, confirming Matsusaka's conjecture for the full modular group.

Findings

Confirmed Matsusaka's conjecture on hyperbolic Eisenstein series

Extended the understanding of Eisenstein series of even weight

Provided new insights into automorphic forms and their analytic properties

Abstract

We prove a conjecture of Matsusaka on the analytic continuationof hyperbolic Eisenstein series in weight $2$ on the full modular group $\mathrm{SL}_2(\mathbb{Z})$.