TY - JOUR
T1 - A p-adic Waldspurger formula
AU - Liu, Yifeng
AU - Zhang, Shouwu
AU - Zhang, Wei
N1 - Publisher Copyright:
© 2018.
PY - 2018/3/15
Y1 - 2018/3/15
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2017-0045
DO - 10.1215/00127094-2017-0045
M3 - Article
AN - SCOPUS:85042701414
SN - 0012-7094
VL - 167
SP - 743
EP - 833
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 4
ER -