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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Author: Santiago Molina
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11F75, 11S40
DOI: https://doi.org/10.1090/tran/7646
Published electronically: May 7, 2019
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Abstract: Let $ A$ be a modular elliptic curve over a totally real field $ F$, and let $ K/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,K)$, 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.


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Additional Information

Santiago Molina
Affiliation: Departament de Matemàtica Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Email: santiago.molina@upc.edu

DOI: https://doi.org/10.1090/tran/7646
Received by editor(s): November 14, 2017
Received by editor(s) in revised form: June 13, 2018
Published electronically: May 7, 2019
Additional Notes: The author was supported in part by DGICYT Grant MTM2015-63829-P. This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 682152).
Article copyright: © Copyright 2019 American Mathematical Society