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

2018/10/27 by Hu, Yueke, Nelson, Paul D. · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.11564

Abstract

In this paper we give quantitative local test vectors for Waldspurger's period integral (i.e., a toric period on GL₂) 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(π×π_χ^-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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• The Weyl bound for Rankin-Selberg L-functions with Joint Ramification

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