A p-ADIC WALDSPURGER FORMULA
نویسندگان
چکیده
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, as a generalization of 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 finite order character, which is outside the range of interpolation, essentially computes the corresponding p-adic torus period.
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