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

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 ${\mathrm{SL}}_2(\mathbb{Z}).$

arXiv commentThe author was notified that the results in this paper was obtained by Dr. Farrell Brumley in his Ph. D. thesis. The author was not aware of this when he posted it on arXiv. Therefore, the author does not intend to submit this paper for publication