A note on a classical relative trace formula

TL;DR

This paper derives a classical relative trace formula to compute the second moment of central values of holomorphic cusp forms, providing a new proof of a known result.

Contribution

It introduces a classical method to derive a relative trace formula for holomorphic cusp forms, offering an alternative proof of Kuznetsov's second moment result.

Findings

Closed formula for the second moment of holomorphic cusp forms' central values

Alternative derivation of Kuznetsov's result using classical methods

Validation of the relative trace formula approach in this context

Abstract

In this note, we derive a relative trace formula (RTF) using classical methods. We obtain a closed formula for the second moment of the central values of holomorphic cusp forms, a result originally established in Kuznetsov's preprint.