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arXiv · 1805.02071

Central Values of $GL(2)\times GL(3)$ Rankin-Selberg $L$-functions with Applications

Qinghua Pi
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Abstract

Let $f$ be a normalized holomorphic cusp form for $SL_2(\mathbb{Z})$ of weight $k$ with $k\equiv0\bmod 4$. By the Kuznetsov trace formula for $GL_3(\mathbb R)$, we obtain the first moment of central values of $L(s,f\otimes \phi)$, where $\phi$ varies over Hecke-Maass cusp forms for $SL_3(\mathbb Z)$. As an application, we obtain a non-vanishing result for $L(1/2,f\otimes\phi)$ and show that such $f$ is determined by $\{L(1/2,f\otimes\phi)\}$ as $\phi$ varies.

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Qinghua Pi. 2018-05-05. Central Values of $GL(2)\times GL(3)$ Rankin-Selberg $L$-functions with Applications. https://arxiv.org/abs/1805.02071

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