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oai:recercat.cat:10459.1/4687682025-10-13T18:08:29Zcom_2072_3622col_2072_479130

2025-10-13T18:08:29Z urn:hdl:10459.1/468768 Exceptional zero formulas for anticyclotomic p-adic L-functions Hernández Barrios, Víctor Molina Blanco, Santiago p-adic L-functions Plectic points Exceptional zero formulas In this note we define anticyclotomic p-adic measures attached to a modular elliptic curve E over a general number field F, a quadratic extension, and a set of places S of F above p. We study the exceptional zero phenomenon that arises when E has multiplicative reduction at some place in S. In this direction, we obtain p-adic Gross-Zagier formulas relating derivatives of the corresponding p-adic L-functions to the extended Mordell-Weil group of E. Our main result uses the recent construction of plectic points on elliptic curves due to Fornea and Gehrmann and generalizes their main result in [9]. We obtain a formula that computes the r-th derivative of the p-adic L-function, where r is the number of places in S where E has multiplicative reduction, in terms of plectic points and Tate periods of E. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 682152). Moreover, the second author has been partially funded by the projects PID2021-124613OB-I00 and PID2022-137605NB-I00 from Ministerio de Ciencia e innovación. We would also like to thank Lennart Gehrmann and Marc Masdeu for all their helpful remarks and comments. 2025-10-13T18:08:29Z 2025-10-13T18:08:29Z 2025 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion http://hdl.handle.net/10459.1/468768 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-124613OB-I00/ES/EL RETO POST-CUANTICO: PROTEGIENDO LA SOCIEDAD CON ISOGENIAS Y CODIGOS/ info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-137605NB-I00/ES/VARIEDADES ABELIANAS, FUNCIONES L Y PUNTOS RACIONALES/ Versió preprint del document publicat a https://doi.org/10.1016/j.jnt.2025.08.015 Journal of Number Theory, 2025, vol. 280, p. 583-633 info:eu-repo/grantAgreement/EC/ERC/682152/EU/BSD (c) Elsevier, 2025 info:eu-repo/semantics/openAccess Elsevier