Anticyclotomic $p$-adic $L$-functions and the exceptional zero phenomenon
Author:
Santiago Molina
Journal:
Trans. Amer. Math. Soc. 372 (2019), 2659-2714
MSC (2010):
Primary 11F75, 11S40
DOI:
https://doi.org/10.1090/tran/7646
Published electronically:
May 7, 2019
MathSciNet review:
3988589
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Abstract | References | Similar Articles | Additional Information
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
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