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New test vector for Waldspurger's period integral, relative trace formula, and hybrid subconvexity bounds
- Publication Year :
- 2018
-
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.<br />Comment: Updated version contains application to relative trace formula computations and hybrid subconvexity bounds
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1810.11564
- Document Type :
- Working Paper