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arXiv · 1404.2354

The Sup-norm of Holomorphic Cusp Forms

Zhilin Ye
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Abstract

Let $f$ be a normalized holomorphic cusp form with a square-free level $N$ and weight $k$. Using a pre-trace formula, we establish a sup-norm bound of $f$ such that $\|y^kf(z)\|_{\infty} \ll N^{-1/6+ε}$ where the trivial bound is $\|y^kf(z)\|_{\infty} \ll 1$. This result is an analog of a similar bound in Maaß form case.

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Zhilin Ye. 2014-04-09. The Sup-norm of Holomorphic Cusp Forms. https://arxiv.org/abs/1404.2354

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