AI 中文总结
本研究针对全纯尖形式的Hecke基，证明其$L^6$范数随权增长的下界，确认Hecke特征形式$L^6$范数不随权趋于无穷而一致收敛，并补充了6次联合质量的相关结果。
AI 中文摘要
设$H_k$是权为$k$的全体全纯尖形式空间的$L^2$规范化Hecke基。我们证明$\textstyle\bigmax_{f \in H_k} \Vert F \Vert_6 \gg (\log\log k)^{\frac{1}{2}}$，其中$F(z) = (\Im z)^{\frac{k}{2}} f(z)$。这证实了当权趋于无穷时，Hecke特征形式的$L^6$范数不会一致收敛。我们还给出了关于6次联合质量的若干结果。
英文摘要
Let $H_k$ be an $L^2$-normalized Hecke basis for the space of all holomorphic cusp forms of weight $k$. We show that $\max_{f\in H_k}\Vert F\Vert_6\gg (\log\log k)^{\frac{1}{2}}$ where $F(z)=(\Im z)^{\frac{k}{2}}f(z).$ This confirms that the $L^6$-norm of Hecke eigenforms does not converge uniformly as the weight goes to infinity. We also give some results on the joint mass of degree $6$.
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