AI 中文总结
本文将Lamzouri关于全纯赫克尖形式最小负本征值n_f下界的结果推广到赫克-马亚斯形式，未假设广义拉马努金猜想，还证明该结果也适用于其对称幂L函数的系数。
AI 中文摘要
近来，Lamzouri对使得赫克本征值λ_f(n_f)<0的最小正整数n_f证明了一个下界，表明对于很多偶整权k的全纯赫克尖形式，n_f≥(log k)^(1-o(1))。本文将Lamzouri的结果推广到赫克-马亚斯形式，未假设广义拉马努金猜想，还进一步证明类似结果也适用于赫克-马亚斯形式的对称幂L函数的系数。
英文摘要
Recently, Lamzouri proved a lower bound for the least positive integer $n_f$ for which the Hecke eigenvalue $λ_f(n_f)<0$, showing it satisfies $n_f \ge (\log k)^{1-o(1)}$ for many holomorphic Hecke cusp forms of even integral weight $k$. In this paper, we extend Lamzouri's result to Hecke-Maass forms without assuming the Generalized Ramanujan Conjecture, and further prove that similar results also hold for the coefficients of symmetric power $L$-functions of Hecke-Maass forms.
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