On the $L^6$-norm of holomorphic Hecke eigenforms

Chengliang Guo, Liangxun Li

Let $H_k$ be an $L^2$-normalized Hecke basis for the space of all holomorphic cusp forms of weight $k$. We show that ${\max }_{f\in H_k}\Vert F{\Vert }_6\gg (\log \log k{)}^{\frac{1}{2}}$ w…