TY - JOUR
T1 - A p-adic Waldspurger formula
AU - Liu, Yifeng
AU - Zhang, Shouwu
AU - Zhang, Wei
N1 - Funding Information:
Liu’s work was partially supported by National Science Foundation (NSF) grant DMS-1302000. S. Zhang’s work was partially supported by NSF grants DMS- 0970100 and DMS-1065839. W. Zhang’s work was partially supported by NSF grants DMS-1301848 and DMS-1601144, and by a Sloan research fellowship.
Funding Information:
We would like to thank Daniel Disegni for his careful reading of the draft version and useful comments. We also thank the anonymous referees for their careful reading and helpful comments which, in particular, led us to the new introduction focusing on the case of rational elliptic curves. Liu's work was partially supported by National Science Foundation (NSF) grant DMS-1302000. S. Zhang's work was partially supported by NSF grants DMS 0970100 and DMS-1065839.W. Zhang's work was partially supported by NSF grants DMS-1301848 and DMS-1601144, and by a Sloan research fellowship
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
VL - 167
SP - 743
EP - 833
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
SN - 0012-7094
IS - 4
ER -