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A zero-density estimate for $L$-functions associated with $\rm GL(3)$ Hecke--Maass cusp forms

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arxiv 2412.02416 v1 pith:5N2MFEPK submitted 2024-12-03 math.NT

Qingfeng Sun , Hui Wang This is my paper · ORCID
classification math.NT
keywords functionsassociatedcuspestimateformshecke--maasszero-densityapplications
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abstract

In this paper, we establish an asymptotic formula for the twisted second moment of $L$-functions associated with Hecke--Maass cusp forms for $\rm SL(3,\mathbb{Z})$, and further deduce a weighted zero-density estimate for these $L$-functions in the spectral aspect which may have important applications in other problems.

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  1. A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application

    math.NT 2025-05 conditional novelty 6.0 of 10

    Selberg-type zero-density estimates for twisted GL2 L-functions yield a central limit theorem for the argument function S(t,f⊗χ) as the character modulus q grows.

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