On \(p\)-adic Waldspurger formula

In this article, we study \(p\)-adic torus periods for certain \(p\)-adic valued functions on Shimura curves coming from classical origin. We prove a \(p\)-adic Waldspurger formula for these periods, generalizing the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we cons...

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Published inarXiv.org
Main Authors Liu, Yifeng, Zhang, Shouwu, Zhang, Wei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.11.2015
Subjects
Dirichlet problem
Interpolation
Toruses
Weight
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Abstract In this article, we study \(p\)-adic torus periods for certain \(p\)-adic valued functions on Shimura curves coming from classical origin. We prove a \(p\)-adic Waldspurger formula for these periods, generalizing the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we construct a new anti-cyclotomic \(p\)-adic \(L\)-function of Rankin-Selberg type. At a character of positive weight, the \(p\)-adic \(L\)-function interpolates the central critical value of the complex Rankin-Selberg \(L\)-function. Its value at a Dirichlet character, which is outside the range of interpolation, essentially computes the corresponding \(p\)-adic torus period.
AbstractList In this article, we study \(p\)-adic torus periods for certain \(p\)-adic valued functions on Shimura curves coming from classical origin. We prove a \(p\)-adic Waldspurger formula for these periods, generalizing the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we construct a new anti-cyclotomic \(p\)-adic \(L\)-function of Rankin-Selberg type. At a character of positive weight, the \(p\)-adic \(L\)-function interpolates the central critical value of the complex Rankin-Selberg \(L\)-function. Its value at a Dirichlet character, which is outside the range of interpolation, essentially computes the corresponding \(p\)-adic torus period.
Author Zhang, Wei
Liu, Yifeng
Zhang, Shouwu
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Snippet In this article, we study \(p\)-adic torus periods for certain \(p\)-adic valued functions on Shimura curves coming from classical origin. We prove a...
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Interpolation
Toruses
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Title On \(p\)-adic Waldspurger formula
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