Large values of modular forms
Large values of modular forms
复制标题
模块化形式的大值
DOI：
10.4310/cjm.2014.v2.n1.a3
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Nicolas Templier
中科院分区：
文献类型：
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作者：
Nicolas Templier
我们证明了在任意大水平N下，存在权值为2的原始全纯模形式f，使得$|f(z)| \gg N^{1/4}$对于某点z，从而反驳了一个民间猜想，即这些形式的上模将小到$N^{0(1)}$。
We show that there are primitive holomorphic modular forms f of weight two and arbitrary large level N such that $|f(z)| \gg N^{1/4}$ for some point z. Thereby we disprove a folklore conjecture that the sup-norm of such forms would be as small as $N^{o(1)}$.