The second moment of $GL(3) \times GL(2)$ $L$-functions, integrated

TL;DR

This paper estimates the second moment of Rankin-Selberg convolution L-functions of fixed SL(3,Z) Maass forms with SL(2,Z) cusp forms, focusing on high degree and large conductors, using long t-aspect integration.

Contribution

It provides a new estimate for the second moment of high-degree L-functions with large conductors in the t-aspect.

Findings

Second moment estimate for degree 12 L-functions.

Analysis of L-functions with conductors of size T^{12}.

Use of long t-aspect integration to obtain results.

Abstract

We consider the family of Rankin-Selberg convolution L-functions of a fixed SL(3, Z) Maass form with the family of Hecke-Maass cusp forms on SL(2, Z). We estimate the second moment of this family of L-functions with a "long" integration in t-aspect. These L-functions are distinguished by their high degree (12) and large conductors (of size T^{12}).