The Zero Density Theorem for the Rankin-Selberg L-function and its applications

TL;DR

This paper proves a zero density theorem for Rankin-Selberg L-functions and applies it to distinguish holomorphic Hecke eigenforms for SL_2(Z).

Contribution

It introduces a new zero density estimate for Rankin-Selberg L-functions and demonstrates its application in identifying holomorphic Hecke eigenforms.

Findings

Established a zero density result for Rankin-Selberg L-functions.

Applied the zero density theorem to distinguish holomorphic Hecke eigenforms.

Enhanced understanding of the distribution of zeros of L-functions.

Abstract

In this work, we establish a zero density result for the Rankin-Selberg $L$-functions. As an application, we apply it to distinguish the holomorphic Hecke eigenforms for $\operatorname{SL}_2(\mathbb{Z}).$