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Abstract: | In this article, we study p-adic torus periods for certain p-adic-valued functions on Shimura curves of classical origin. We prove a p-adic Waldspurger formula for these periods as a generalization of 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 finite-order character, which is outside the range of interpolation, essentially computes the corresponding p-adic torus period. |
Publication Date: | 15-Mar-2018 |
Electronic Publication Date: | 9-Feb-2018 |
Citation: | Liu, Yifeng, Zhang, Shouwu, Zhang, Wei. (2018). A p-ADIC WALDSPURGER FORMULA. DUKE MATHEMATICAL JOURNAL, 167 (743 - 833). doi:10.1215/00127094-2017-0045 |
DOI: | doi:10.1215/00127094-2017-0045 |
ISSN: | 0012-7094 |
EISSN: | 1547-7398 |
Pages: | 743 - 833 |
Type of Material: | Journal Article |
Journal/Proceeding Title: | DUKE MATHEMATICAL JOURNAL |
Version: | Author's manuscript |
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