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arXiv · 2308.11114

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

Zhining Wei·Shifan Zhao
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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.

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Zhining Wei, Shifan Zhao. 2023-08-22. On Möbius functions from automorphic forms and a generalized Sarnak's conjecture. https://arxiv.org/abs/2308.11114

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