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arXiv · 2411.16953

On the Fourier expansion of Gan-Gurevich lifts on the exceptional group of type $G_2$

Henry H. Kim·Takuya Yamauchi
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Abstract

By using the degenerate Whittaker functions, we study the Fourier expansion of the Gan-Gurevich lifts which are Hecke eigen quaternionic cusp forms of weight $k$ ($k\geq 2$, even) on the split exceptional group $G_2$ over $\mathbb{Q}$ which come from elliptic newforms of weight $2k$ without supercuspidal local components. In particular, our results give a partial answer to Gross' conjecture.

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Henry H. Kim, Takuya Yamauchi. 2024-11-25. On the Fourier expansion of Gan-Gurevich lifts on the exceptional group of type $G_2$. https://arxiv.org/abs/2411.16953

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