English

On M\"obius functions from automorphic forms and a generalized Sarnak's conjecture

Number Theory 2023-08-23 v1

Abstract

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

Keywords

Cite

@article{arxiv.2308.11114,
  title  = {On M\"obius functions from automorphic forms and a generalized Sarnak's conjecture},
  author = {Zhining Wei and Shifan Zhao},
  journal= {arXiv preprint arXiv:2308.11114},
  year   = {2023}
}

Comments

13 pages

R2 v1 2026-06-28T12:01:00.109Z