Heegner points and Eisenstein series

TL;DR

This paper presents a new method for computing the twisted second moment of critical values of class group L-functions for imaginary quadratic fields, simplifying calculations and confirming expected growth patterns.

Contribution

It introduces an alternative approach that avoids lengthy calculations and accurately predicts polynomial growth in the s-parameter.

Findings

Simplified computation of the twisted second moment.

Confirmed polynomial growth in the s-parameter.

Provides an efficient method for analyzing class group L-functions.

Abstract

We give an alternative computation of the twisted second moment of critival values of class group $L$-functions attached to an imaginary quadratic field. The method avoids long calculations and yields the expected polynomial growth in the $s$-parameter for the remaining term.