Anticyclotomic p-adic l-functions and the exceptional zero phenomenon
Number Theory
2018-06-29 v3
Abstract
Let A be a modular elliptic curve over a totally real field F, and let E/F be a totally imaginary quadratic extension. In the event of exceptional zero phenomenon, we prove a formula for the derivative of the multivariable anticyclotomic p-adic L-function attached to (A,E), in terms of the Hasse-Weil L-function and certain p-adic periods attached to the respective automorphic forms. Our methods are based on a new construction of the anticyclotomic p-adic L-function by means of the corresponding automorphic representation.
Cite
@article{arxiv.1509.08617,
title = {Anticyclotomic p-adic l-functions and the exceptional zero phenomenon},
author = {Santiago Molina Blanco},
journal= {arXiv preprint arXiv:1509.08617},
year = {2018}
}