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arXiv · 2305.11492

Results on the Non-Vanishing of Derivatives of L-Functions of Vector-Valued Modular Forms

Subong Lim·Wissam Raji
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Abstract

We show a non-vanishing result for the averages of the derivatives of $L$-functions associated with the orthogonal basis of the space of vector-valued cusp forms of weight $k\in \frac12 \mathbb{Z}$ on the full group in the critical strip. We also show the existence of at least one basis element whose $L$-function does not vanish under certain conditions. As an application, we generalize our result to Kohnen's plus space and prove an analogous result for Jacobi forms.

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Subong Lim, Wissam Raji. 2023-05-19. Results on the Non-Vanishing of Derivatives of L-Functions of Vector-Valued Modular Forms. https://doi.org/10.1017/s001309152400052x

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