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arXiv · 1810.11564

New test vector for Waldspurger's period integral, relative trace formula, and hybrid subconvexity bounds

Yueke Hu·Paul D. Nelson
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Abstract

In this paper we give quantitative local test vectors for Waldspurger's period integral (i.e., a toric period on $\text{GL}_2$) in new cases with joint ramifications. The construction involves minimal vectors, rather than newforms and their variants. This paper gives a uniform treatment for the matrix algebra and division algebra cases under mild assumptions, and establishes an explicit relation between the size of the local integral and the finite conductor $C(\pi\times\pi_{\chi^{-1}})$. As an application, we combine the test vector results with the relative trace formula, and prove a hybrid type subconvexity bound which can be as strong as the Weyl bound in proper range.

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Yueke Hu, Paul D. Nelson. 2018-10-27. New test vector for Waldspurger's period integral, relative trace formula, and hybrid subconvexity bounds. https://arxiv.org/abs/1810.11564

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