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Anticyclotomic p-adic L-functions and the exceptional zero phenomenon

Author
Molina, S.
Type of activity
Journal article
Journal
Transactions of the American Mathematical Society
Date of publication
2019-08-15
Volume
372
Number
4
First page
2659
Last page
2714
DOI
10.1090/tran/7646
Repository
http://hdl.handle.net/2117/168795 Open in new window
https://arxiv.org/abs/1509.08617 Open in new window
URL
https://www.ams.org/journals/tran/2019-372-04/S0002-9947-2019-07646-8/ Open in new window
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 ...

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