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 -functions: Rankin-Selberg -functions of symmetric powers of distinct holomorphic cusp forms and -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.
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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}
}
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13 pages