On Möbius functions from automorphic forms and a generalized Sarnak's conjecture

2023/08/22 by Wei, Zhining, Zhao, Shifan
#11F30 #11F66 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2308.11114

Abstract

In this paper, we consider Möbius functions associated with two types of L-functions: Rankin-Selberg L-functions of symmetric powers of distinct holomorphic cusp forms and L-functions of Maass cusp forms. We show that these Möbius functions are weakly orthogonal to bounded sequences. As a direct corollary, a generalized Sarnak's conjecture holds for these two types of Möbius functions.

Related

• Selberg's Central Limit Theorem for automorphic L-functions in the t-aspect
• The universality of symmetric power L-functions and their Rankin-Selberg L-functions
• Möbius orthogonality for q-semimultiplicative sequences
• A remark on Sarnak's conjecture
• The Ramanujan-Petersson and Selberg conjectures for Maass forms