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arXiv · 2608.02234

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

Chengliang Guo·Liangxun Li
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Abstract

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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Chengliang Guo, Liangxun Li. 2026-08-03. On the $L^6$-norm of holomorphic Hecke eigenforms. https://arxiv.org/abs/2608.02234

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