Abstract
Suppose that \(\pi\) is a unitary cuspidal automorphic representation of \(GL_r(\mathbb{A}_{\mathbb{Q}})\) and \(L(s,\pi)\) is the automorphic \(L\)-function related to \(\pi\), For \({\frac{1}{2}<\sigma<1}\), let \(m(\sigma) \geq 2\) be the supremum of all numbers \(m\) such that
We are interested in the lower bound of \(m(\sigma)\) for \(1-\frac{1}{r}<\sigma<1\) . Then as an application, we establish asymptotic formulas for the second, fourth and sixth power moments of \(L(s,\pi)\).
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This work is supported by National Natural Science Foundation of China (Grant No. 12171286).
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Huang, J. Higher moments of automorphic \(L\)-functions of \(GL(r)\) and its applications. Acta Math. Hungar. 169, 489–502 (2023). https://doi.org/10.1007/s10474-023-01324-8
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DOI: https://doi.org/10.1007/s10474-023-01324-8