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arXiv · 1906.06103

Simple Fourier Trace Formulas of Cubic Level and Applications

Qinghua Pi·Yingnan Wang·Lei Zhang
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Abstract

With the method of the relative trace formula and the classification of simple supercuspidal representations, we establish some Fourier trace formulas for automorphic forms on $PGL(2)$ of cubic level. As applications, we obtain a non-vanishing result for central $L$-values of holomorphic newforms and a weighted Weyl's law for Maass newforms.

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Qinghua Pi, Yingnan Wang, Lei Zhang. 2019-06-14. Simple Fourier Trace Formulas of Cubic Level and Applications. https://arxiv.org/abs/1906.06103

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