Work

A p-adic Waldspurger formula

Year: 2018

Type: article

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.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2017-0045

Authors: Yifeng Liu, Shouwu Zhang, Wei Zhang

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Periods and special values of L-functions for unitary groups, FRG: Collaborative Research: Periods of Automorphic Forms and Applications to L- Functions, Topics in arithmetic algebraic geometry, Algebraic Cycles and L-functions

OpenAlex ID: W2173089136

FWCI: 3.867

Cites: 22

Cited by: 29

Related to: