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 in | arXiv.org |
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Main Authors | , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
25.11.2015
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1511.08172 |